The homebrew package doublepagefloats needed for my first answer -- unfortunately, it is too long to fit in my answer as well:
\NeedsTeXFormat{LaTeX2e}[1994/06/01]%
\ProvidesPackage{doublepagefloats}[%
2023/06/22
v0.1
double page floats]%
\extrafloats{20}% Techniques used in this package include generating quite some "invisible floats", which may prolong the queue
\newif\ifsymmbound\symmboundfalse% Text boundaries on left and right page of double page float different because of caption
\newif\ifleftcaption\leftcaptionfalse% Caption on right or left page?
\DeclareOption{symmbound}{\symmboundtrue}% With option [symmboundtrue] text boundaries equal on both pages
\DeclareOption{leftcaption}{\leftcaptiontrue}% With option [symmboundtrue] text boundaries equal on both pages
\DeclareOption*{\OptionNotUsed}% Warning, that option is not used
\ProcessOptions\relax%
\RequirePackage{adjustbox}% Delivers package{graphicx}
\RequirePackage{zref-abspage,zref-user, zref-pageattr}% Needed for zlabel{} and the mechanism, to erase foot or head of page
\RequirePackage[maxfloats=256]{morefloats}% For not getting the error "too many unprocessed floats"
\maxdeadcycles=200% An error "too many dead cycles" sometimes can occur because of the cycles in \pushfloattopage{}
% Exchange of \belowcaptionskip and \abovecaptionskip for caption above figure:
\newcommand\exch@ngec@ptionskip{%
\let\dpf@templen\abovecaptionskip%
\let\abovecaptionskip\belowcaptionskip%
\let\belowcaptionskip\dpf@templen}%
% Width of the gap between the text on the left and the text on the right page:
\newcommand\gapwidth{\dimexpr\paperwidth-\evensidemargin+\oddsidemargin-\textwidth\relax}%
% Savebox for caption:
\newsavebox{\dpf@captionbox}%
% Left half of the image (originally overtaken from Martin Scharrer, all mistakes by me):
\newcommand\leftp@geflo@t[5][\@empty]{% #1 auxiliary caption, #2: b/t, #3: p/l, #4: content, #5: caption
\if #2t\else%
\if #2h\else%
\exch@ngec@ptionskip% For bottom floats with above caption a skip below the caption is needed instead of above
\fi%
\fi%
\if #2t%
\vskip-\dimexpr1in+\voffset+\topmargin+\headheight+\headsep\relax% Move float directly to top of page
\fi%
\ifx\@empty#1%
\global\savebox{\dpf@captionbox}{\parbox[b]{\textwidth}{\caption[#5]{#5}}}% This works, if #1 is empty
\else%
\global\savebox{\dpf@captionbox}{\parbox[b]{\textwidth}{\caption[#1]{#5}}}% This doesn't work, if #1 is empty, why?
\fi%
\if #2t\else%
\if #2h\else%
\ifleftcaption%
\usebox{\dpf@captionbox}\\%
\else%
\ifsymmbound% Text on both pages symmetrical?
\rule{0pt}{\ht\dpf@captionbox}\\% this delivers the same white space as the height of the caption
\fi%
\fi%
\fi%
\fi%
\makebox[\textwidth][r]{%
\if #3p\relax%
\global\let\panowidth\paperwidth%
\else%
\global\let\panowidth\linewidth%
\fi%
\makebox[\textwidth][r]{%
\adjustbox{trim=0 0 {.5\width} 0,clip}{#4}}% End \adjustbox
\if #3p%
\hskip-\dimexpr\paperwidth-\textwidth-1in-\hoffset-\evensidemargin\relax%
\fi%
}%
\if #2b\else%
\if #2l\else%
\ifleftcaption%
\\\usebox{\dpf@captionbox}%
\else%
\ifsymmbound% Text on both pages symmetrical?
\\\rule{0pt}{\ht\dpf@captionbox}% this delivers the same white space as the height of the caption
\fi%
\fi%
\fi%
\fi%
\if #2b%
\vskip-\dimexpr\paperheight-\textheight-1in-\voffset-\topmargin-\headheight-\headsep\relax% Move float completely to page bottom
\fi%
}% Ende \leftp@geflo@t
% Right half of the image (originally overtaken from Martin Scharrer, all mistakes by me):
\newcommand*\rightp@geflo@t[5][\@empty]{% #1: auxiliary caption, #2: b/t, #3: p/l, #4: content, #5: caption
\if #2t\else%
\if #2h\else%
\exch@ngec@ptionskip% For bottom floats with above caption a skip below the caption is needed instead of above
\fi%
\fi%
\if #2t%
\vskip-\dimexpr1in+\voffset+\topmargin+\headheight+\headsep\relax%
\fi%
\ifx\@empty#1%
\global\savebox{\dpf@captionbox}{\parbox[b]{\textwidth}{\caption[#5]{#5}}}% This works, if #1 is empty
\else%
\global\savebox{\dpf@captionbox}{\parbox[b]{\textwidth}{\caption[#1]{#5}}}% This doesn't work, if #1 is empty, why?
\fi%
\if #2t\else%
\if #2h\else%
\ifleftcaption%
\ifsymmbound% Text on both pages symmetrical?
\rule{0pt}{\ht\dpf@captionbox}\\% this delivers the same white space as the height of the caption
\fi%
\else%
\usebox{\dpf@captionbox}\\%
\fi%
\fi%
\fi%
\makebox[\textwidth][l]{%
\if #3p%
\global\let\panowidth\paperwidth%
\hskip-\dimexpr1in+\hoffset+\oddsidemargin\relax%
\else%
\global\let\panowidth\linewidth%
\fi%
\adjustbox{trim={.5\width} 0 0 0,clip}{#4}% End \adjustbox
}% end of \makebox
\if #2b\else%
\if #2l\else%
\ifleftcaption%
\ifsymmbound% Text on both pages symmetrical?
\\\rule{0pt}{\ht\dpf@captionbox}% this delivers the same white space as the height of the caption
\fi%
\else%
\\\usebox{\dpf@captionbox}%
\fi%
\fi%
\fi%
\if #2b%
\vskip-\dimexpr\paperheight-\textheight-1in-\voffset-\topmargin-\headheight-\headsep\relax%
\fi%
}% Ende \rightp@geflo@t
%----------------------------------------
% With this we can push a float forward to a certain page
%----------------------------------------
\newcount\invisiblefloat%
\invisiblefloat=0%
\newcount\safety%
\safety=0
\newcommand\dpf@position{}% Dummy for being able to call for \renewcommand
\def\pushfloattopage#1#2#3{% #1: page to reach, #2: float type (figure/table), #3: float placement
\loop\ifnum\safety<20%
\edef\pagelastinvisiblefloat{\zref@extractdefault{invisiblefloat\number\invisiblefloat}{abspage}{-1}}%
\advance\invisiblefloat by 1\relax% increment label number for unique label
\edef\actualpage{\zref@extractdefault{invisiblefloat\number\invisiblefloat}{abspage}{-1}}%
% Invisible float without caption, needing no space, delivers information about actual page
\if #3h
\renewcommand\dpf@position{t}
\begin{@float}{#2}[t]% Empty float without \caption, so \counter{figure/table} is not increased
\else%
\if #3l
\renewcommand\dpf@position{b}
\begin{@float}{#2}[b]% Empty float without \caption, so \counter{figure/table} is not increased
\else%
\renewcommand\dpf@position{#3}%
\begin{@float}{#2}[#3]% Empty float without \caption, so \counter{figure/table} is not increased
\fi%
\fi%
% If either following another invisible float or it is the landing page #1 (then the doublepage float follows), compensate \floatsep, either \textfloatsep
\ifnum\actualpage = \pagelastinvisiblefloat\relax%
\vskip-\floatsep%
\else%
\ifnum\actualpage=#1\relax%
\vskip-\floatsep%
\else%
\vskip-\textfloatsep%
\fi%
\fi%
\zlabel{invisiblefloat\number\invisiblefloat}% test label: On which page are we?
\end{@float}%
% Error queries:
\ifnum\actualpage = -1\relax% Label not found
\PackageWarning{doublepagefloats}{Label of invisible float not found}%
\let\iterate\relax% leave the loop
\fi%
\edef\lastpage{\zref@extractdefault{LastPage}{abspage}{-1}}
\ifnum#1>\lastpage\relax% #1 > last page
\PackageWarning{doublepagefloats}{Page number #1 behind last page \lastpage}%
\let\iterate\relax% leave the loop
\fi% if #1 > last page
\ifnum#1 < 1\relax% Too small argument #1
\PackageWarning{doublepagefloats}{Absolute page number less than 1 does not exist}%
\let\iterate\relax% leave the loop
\fi%
% Normal end of loop after landing page is reached
\ifnum\numexpr#1-1\relax < \actualpage%
\let\iterate\relax% leave the loop
\fi%
\advance\safety by 1\relax%
\repeat%
\safety=0% for next call to pushfloattopage
}% End \pushfloattopage
%----------------------------------------
% Make a length non-elastic
%----------------------------------------
\newdimen\dpf@fixedlength% \newdimen delivers a non-elastic length
\newcommand\makefixedlength[1]{%
\setlength\dpf@fixedlength{#1}% copying length to non-elastic one strips off the elastic part
\global\setlength{#1}\dpf@fixedlength}% now copying back
%----------------------------------------
% \doublepagefloat{figure/table}{b/t/h/l}{p/l}{<content>{<caption>} is the new user command, to generate one or more double page floats
%----------------------------------------
\newcommand\dpf@pagebeforestart{-2}%
\newcounter{l@belnumber}% generates distinctive numbers for generating individual labels
\newcounter{dpf@l@belnumbershipout}% same for the shipout routine
\stepcounter{dpf@l@belnumbershipout}% start with 1
% For \label-\ref-mechanism to determine the right page number floats get an additional label dpf@float made unique by prolonging with the reading of a new counter "dpf@float"
\newcounter{dpf@float}% Counter for labeling every float (as the change of totalnumber will affect every float as well, independent of float type)
\let\end@floatold\end@float% Save original end of envíronment @float
\def\end@float{%
\stepcounter{dpf@float}% So starting with one
\zlabel{dpf@float\arabic{dpf@float}}%
\end@floatold%
}%
% Save counter totalnumber
\AtBeginDocument{% Changes in the preamble will be taken into account as well, as we only save the counter at begin of document
\expandafter\edef\expandafter\totalnumber@old\expandafter{\the\value{totalnumber}}% Save state of counter totalnumber
}%
\newcommand*{\doublepagefloat}[6][\@empty]{% #1: auxiliary caption, #2: figure/table, #3: b/t/h/l, #4: p/l, #5: content, #6: caption
%\newcommand*\doublepagefloat[5]{% #1: figure/table, #2: b/t/h/l, #3: p/l, #4: content, #5: caption, #6: auxiliary caption
% #1: auxiliary caption, the one for the list of figures
% #2: floattype, usually figure or table
% #3: b: (b)ottom of page
% t: (t)op of page
% h: (h)igh, i.e. top of text
% l: (l)ow, i.e. bottom of text
%
% #4: p: (p)aper, i.e. the content may be up to 2\paperwidth wide, will be centered to the gap between both pages and may stretch till the paper boundaries.
% It may be narrower though and then will still center. If the width of the content is exactly \doubletextwidth, it stretches from the left border of the left page text to the right border of the right page
% text.
% l: (l)ine, i.e. the content only uses the width of a line on both pages with a wide gap between both parts
% #5: content, i.e. the image itself
% #6: main caption, the text under the image
% Page number of last float before:
\ifnum\value{dpf@float}=0\relax% This will become the first float?
\newcommand\dpf@pagelastfloat{0}% fictitious page of last float
\else%
\expandafter\edef\expandafter\dpf@pagelastfloat\expandafter{\zref@extractdefault{dpf@float\arabic{dpf@float}}{abspage}{-1}}% must be expanded, before counter dpf@float is stepped again
\fi%
% Page, where \doublepagefloat was run (double page float is now available)
\stepcounter{l@belnumber}% the next label should have another number (so counter starts with 1)
\zlabel{dpf@run\arabic{l@belnumber}}% Unique label
\expandafter\edef\expandafter\dpf@runpage\expandafter{\zref@extractdefault{dpf@run\arabic{l@belnumber}}{abspage}{-1}}% must be expanded, before counter l@belnumber is stepped again
% The double page float can only appear on the first coming even page and after the last float before was printed and after \doublepagefloat was run. Calculated is the page BEFORE the first double float page
\expandafter\edef\expandafter\dpf@pagebeforestart\expandafter{\dpf@pagelastfloat}% here the last float was printed
\ifnum\dpf@pagebeforestart < \dpf@runpage\relax%
\expandafter\renewcommand\expandafter\dpf@pagebeforestart\expandafter{\dpf@runpage}%
\fi%
\ifodd\dpf@pagebeforestart\relax% Then the double page float may already start at the next page
\else% otherwise inkrement by 1 to reach an odd page number
\expandafter\edef\expandafter\dpf@temp\expandafter{\dpf@pagebeforestart}%
\expandafter\expandafter\expandafter\edef\expandafter\expandafter\expandafter\dpf@pagebeforestart\expandafter\expandafter\expandafter{\expandafter\numexpr\dpf@temp +1\relax}%
\fi%
% Store special pages globally with unique name for later use
\expandafter\global\expandafter\edef\csname dpf@pagebeforestart\arabic{l@belnumber}\endcsname{\dpf@pagebeforestart}% Globally stored under unique name for comparison in next run
\expandafter\global\expandafter\edef\csname dpf@pagelastfloat\arabic{l@belnumber}\endcsname{\dpf@pagelastfloat}% Globally stored under unique name for altering \floatsep
% Now push both halves of double page float to the appropriate pages and print them:
\edef\dpf@lastpage{\zref@extractdefault{LastPage}{abspage}{-1}}%
\expandafter\pushfloattopage\expandafter{\numexpr\dpf@pagebeforestart +1\relax}{#2}{#3}%
\if #3h%
\begin{@float}{#2}[!t]% printing the left half of the image ...
\else%
\if #3l%
\begin{@float}{#2}[!b]% printing the left half of the image ...
\else%
\begin{@float}{#2}[!#3]% printing the left half of the image ...
\fi\fi%
\leftp@geflo@t[#1]{#3}{#4}{#5\if#3h\else\if#3l\else\zlabel{left#3\arabic{l@belnumber}}\fi\fi}{#6}% Set label only in cases t/b, not in cases h/l
\end{@float}%
\expandafter\pushfloattopage\expandafter{\numexpr\dpf@pagebeforestart +2\relax}{#2}{#3}%
\if #3h%
\begin{@float}{#2}[!t]% ... and now the right half
\else%
\if #3l%
\begin{@float}{#2}[!b]% ... and now the right half
\else%
\begin{@float}{#2}[!#3]% ... and now the right half
\fi\fi%
\rightp@geflo@t[#1]{#3}{#4}{#5\if#3h\else\if#3l\else\zlabel{right#3\arabic{l@belnumber}}\fi\fi}{#6}% Set label only in cases t/b, not in cases h/l
\end{@float}%
}% End of \doublepagefloat
%-------------------------------
% Manipulate counters totalnumber and dpf@erase as well as lengths \floatsep and \textfloatsep via Hooks according to the calculations before
% (after an idea of John Kormylo and with the help of Ulrike Fischer):
% totalnumber: Helps against other floats on the last double float page in a row (or of a single double page float) if set to 2
% -- and if the double page float is set to the top of the page, not the bottom!
% dpf@erase: controls erasing of page head or foot for placement parameters t and b
% lengths \floatsep and \textfloatsep: Are temporarily stripped off their elastic parts for better "invisibility" of "invisible floats" and
% better symmetric appearance of left and right page text in combination with a double page float -- are set back to their original
% elastic values later
%-------------------------------
\newlength\dpf@floatsepelastic%
\setlength\dpf@floatsepelastic{\floatsep}% Save floatsep
\newlength\dpf@textfloatsepelastic%
\setlength\dpf@textfloatsepelastic{\textfloatsep}% Save textfloatsep
\def\dpf@nextpage{-1}% Initializing: Next page (=0) doesn't exist
\AddToHook{shipout/after}{% With "after" we are sure to redo changes on the second page of the double page float before
% let \textfloatsep unaltered for two pages in total, before setting back
\ifnum\dpf@nextpage > 0% If following page shall have fixed \textfloatsep as well, \dpf@nextpage is positive
\xdef\dpf@nextpage{0}% Here set back to 0, because only one further page shall have fixed \textfloatsep
\makefixedlength{\floatsep}% Strip off the elastic part of \floatsep
\makefixedlength{\textfloatsep}% Strip off the elastic part of \textfloatsep
\else%
\setlength\floatsep\dpf@floatsepelastic% restore elastic length \floatsep
\setlength\textfloatsep\dpf@textfloatsepelastic% restore elastic length \textfloatsep
\fi%
\ifnum\value{l@belnumber} > \numexpr\value{dpf@l@belnumbershipout} - 1\relax\relax% l@belnumber >= dpf@l@belnumbershipout ?
\expandafter\expandafter\expandafter\ifnum\csname dpf@pagebeforestart\arabic{dpf@l@belnumbershipout}\endcsname = \value{page}% After shipout of the page before the double page float (for the first double page float page) ...
\setcounter{totalnumber}{2}% ... set totalnumber=2 (1 invisible float, one half of the double page float, more are forbidden)
\fi%
% Make \textfloatsep unelastic, to make invisible floats invisible be compensating their own length (not exactly possible with elastic lengths)
\expandafter\expandafter\expandafter\ifnum\csname dpf@pagelastfloat\arabic{dpf@l@belnumbershipout}\endcsname = \value{page}% Page of last float before double page float
\makefixedlength{\floatsep}% Strip off the elastic part of \floatsep
\makefixedlength{\textfloatsep}% Strip off the elastic part of \textfloatsep
\xdef\dpf@nextpage{1}%
\fi%
\ifnum\numexpr\value{page}+1\relax = \zref@extractdefault{leftt\arabic{dpf@l@belnumbershipout}}{page}{-1}% Left side with t- or h-double page float
\makefixedlength{\floatsep}% Strip off the elastic part of \floatsep
\makefixedlength{\textfloatsep}% textfloatsep now non-elastic, making calculations easier
\xdef\dpf@nextpage{1}%
\fi%
\ifnum\numexpr\value{page}+1\relax = \zref@extractdefault{leftb\arabic{dpf@l@belnumbershipout}}{page}{-1}% Left side with l- or b-double page float
\makefixedlength{\floatsep}% Strip off the elastic part of \floatsep
\makefixedlength{\textfloatsep}% textfloatsep now non-elastic, making calculations easier
\xdef\dpf@nextpage{1}%
\fi%
\fi%
}%
\AddToHook{shipout/before}{% With "before" we are sure that these changes on the second page of the double page float can be redone by a directly following second douböle page float
% Set counter dpf@erase =0 on normal pages, =1 for pages with pagewide double page float in the head (leftt, rightt) and =2 for pages with pagewide double page float in the foot (leftb, rightb)
\setcounter{dpf@erase}{0}% For normal pages
\ifnum\value{l@belnumber} > \numexpr\value{dpf@l@belnumbershipout} - 1\relax\relax% If label exists already
% Erase head or bottom of page in case of a double page float, that spans the complete page (\paperwidth)
\ifnum\numexpr\value{page} + 1\relax = \zref@extractdefault{leftt\arabic{dpf@l@belnumbershipout}}{page}{-1}\setcounter{dpf@erase}{1}\fi%
% If on left page of double page float (top): Erase head (dpf@erase=1)
\ifnum\numexpr\value{page} + 1\relax = \zref@extractdefault{rightt\arabic{dpf@l@belnumbershipout}}{page}{-1}\setcounter{dpf@erase}{1}\fi%
% If on right page of double page float (top): Erase head (dpf@erase=1)
\ifnum\numexpr\value{page} + 1\relax = \zref@extractdefault{leftb\arabic{dpf@l@belnumbershipout}}{page}{-1}\setcounter{dpf@erase}{2}\fi%
% If on left page of double page float (bottom): Erase bottom (dpf@erase=2)
\ifnum\numexpr\value{page} + 1\relax = \zref@extractdefault{rightb\arabic{dpf@l@belnumbershipout}}{page}{-1}\setcounter{dpf@erase}{2}\fi%
% If on right page of double page float (bottom): Erase bottom (dpf@erase=2)
% Set totalnumber to original value
\expandafter\expandafter\expandafter\ifnum\expandafter\numexpr\csname dpf@pagebeforestart\arabic{dpf@l@belnumbershipout}\endcsname + 2\relax = \value{page}% After shipout of the page before the double page float (for the first double page float page) ...
\setcounter{totalnumber}{\totalnumber@old}% ... set totalnumber=2 (1 for invisible float, one half of the double page float)
\fi%
% Step labelcounter
\expandafter\expandafter\expandafter\ifnum\expandafter\numexpr\csname dpf@pagebeforestart\arabic{dpf@l@belnumbershipout}\endcsname + 1\relax = \value{page}% After shipout of the page before the double page float (for the first double page float page) ...
\stepcounter{dpf@l@belnumbershipout}% step label counter
\fi%
\fi% If label exists already
}% \AddToHook{shipout/before}
%----------------------------------------
% Mechanism for erasing page head or foot based on idea by Ulrike Fischer (see https://tex.stackexchange.com/questions/689322/how-to-transport-code-not-material-with-a-float)
% The counter dpf@erase is set in \AddToHook{shipout/before} according to labels in the double page floats themselves, set in doublepagefloats
%----------------------------------------
\newcounter{dpf@erase}%
% Counter dpf@erase (controlled by shipout/before, see above) controls, whether page head (1), foot (2) or nothing (0) is erased. In the latter case the original macro is called
\AtBeginDocument{% That way one can change head and foot in the preamble
% Save original head and foot of page
\let\@evenheadold\@evenhead% Save even head
\let\@oddheadold\@oddhead% Save odd head
\let\@evenfootold\@evenfoot% Save even foot
\let\@oddfootold\@oddfoot% Save odd foot
% Dependand on counter dpf@erase don't show saved head or foot of page, reset dpf@erase immediately, so that the suppression lasts just for one page
\def\@evenhead{\ifnum\value{dpf@erase} = 1\relax\else\@evenheadold\fi}% Take saved even head, if not page of labeled figure
\def\@oddhead{\ifnum\value{dpf@erase} = 1\relax\else\@oddheadold\fi}% Take saved odd head, if not page of labeled figure
\def\@evenfoot{\ifnum\value{dpf@erase} = 2\relax\else\@evenfootold\fi}% Take saved even foot, if not page of labeled figure
\def\@oddfoot{\ifnum\value{dpf@erase} = 2\relax\else\@oddfootold\fi}% Take saved odd foot, if not page of labeled figure
}% AtBeginDocument
\endinput%
