This is caused by the fact that TeX4ht now uses the pgfsys-dvisvgm4ht.def driver by default. It doesn't support the external library. Here is the version that fixes this issue:
% Copyright 2021 by Michal Hoftich
% Copyright 2006 by Till Tantau
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Public License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
\ProvidesFileRCS{pgfsys-dvisvgm4ht.def}
% Driver commands for tex4ht
%
% Load common pdf commands:
%
% we load the dvips driver by default. it doesn't support patterns and some other stuff,
% but it handles better nested images and some formatting. if you use patterns or if you
% have other issues with the default method, pass the "tikz-dvisvgm" option to make4ht.
\ifdefined\ifOption
\ifOption{tikz+}{\input pgfsys-dvisvgm.def}{\input pgfsys-dvips.def}
\else
% load the dvips driver by default
\input pgfsys-dvips.def
\fi
\def\texfourht@tikz@begin{%
\bgroup%
\def\run@pict@cmd{}% insert the \Picture hooks only in the top nesting level
\def\end@pict@cmd{}%
\ifdefined\EndPicture\else% We are already inside command that uses \Picture
\ifdefined\inside@pict@cmd\else% handle nested uses
\ifdefined\tikzexternalize\else% Support externalize library
\def\run@pict@cmd{\Picture*}%
\def\end@pict@cmd{\EndPicture}%
\fi\fi\fi%
% command used to detect nesting
\def\inside@pict@cmd{}%
\csname a:tikzpicture\endcsname%
}
\def\texfourht@tikz@end{%
\csname b:tikzpicture\endcsname%
\egroup%
}
\AtBeginDocument{%
\NewConfigure{tikzpicture}{2}%
\catcode`\:=11%
\Configure{tikzpicture}{%
\protect\csname nested:math\endcsname% support display math
\run@pict@cmd{}%
}{\end@pict@cmd}
% configure the output picture format to svg, as it will require dvisvgm
% post processing.
\Configure{Picture}{.svg}%
% insert tex4ht hooks around TikZ picture box
\def\pgfsys@typesetpicturebox#1{%
\texfourht@tikz@begin%
\orig@pgfsys@typesetpicturebox{#1}%
\texfourht@tikz@end%
}
%
\ConfigureEnv{tikzpicture}{\texfourht@tikz@begin}{\texfourht@tikz@end}{}{}%
\ConfigureEnv{pgfpicture}{\texfourht@tikz@begin}{\texfourht@tikz@end}{}{}%
\catcode`\:=12%
}
% Make the code inserted by tex4ht configurable
%
\let\orig@pgfsys@typesetpicturebox\pgfsys@typesetpicturebox
%\def\pgf@sys@postscript@header#1{{\special{! #1}}}
\endinput
%%% Local Variables:
%%% mode: latex
%%% End:
I've also found that you have one issue in your TeX file. You have spurious comma after \includegraphics command. It ends in the HTML code. This is a fixed version:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{external}
\ifdefined\HCode
% this part is activated with make4ht
\tikzexternalize[mode=only graphics]
\tikzset{png export/.style={
/pgf/images/external info,
/pgf/images/include external/.code={%
\includegraphics{##1.png}
},
},
png export,
}
\else
% this part is activated with pdflatex
\tikzexternalize
\tikzset{pdf export/.style={
/pgf/images/external info,
/pgf/images/include external/.code={%
\includegraphics{##1.pdf},
},
},
pdf export,
}
\fi
\begin{document}
\begin{tikzpicture}
\draw (0,0) -- (0,1) -- (1,1) -- (1,0) -- (0,0);
\end{tikzpicture}
\end{document}
Btw, TeX4ht has built-in support for the externalization library, it always requires the picture mode. The current version is somehow broken, but you can try this fix, tikz-hooks.4ht:
% tikz-hooks.4ht (2021-10-21-14:55), generated from tex4ht-4ht.tex
% Copyright 2021 TeX Users Group
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
% version 1.3c of this license or (at your option) any
% later version. The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions
% of LaTeX version 2005/12/01 or later.
%
% This work has the LPPL maintenance status "maintained".
%
% The Current Maintainer of this work
% is the TeX4ht Project <http://tug.org/tex4ht>.
%
% If you modify this program, changing the
% version identification would be appreciated.
\immediate\write-1{version 2021-10-21-14:55}
\ifdefined\pgfsysdriver\else%
\typeout{*****************************}
\typeout{TeX4ht info: Using dvisvgm4ht TikZ driver. Put \detokenize{\def\pgfsysdriver{driver-name}} to your
document before use of TikZ if you want to another driver. Use tikz+ option if your TikZ pictures use patterns.}%
\def\pgfsysdriver{pgfsys-dvisvgm4ht.def}%
\fi%
\:AtEndOfPackage{%
\let\use:tikzlibrary\usetikzlibrary
\def\find:externalize#1external#2\@nil{%
\ifdefined\tikzexternalize
\let\tikz:externalize\tikzexternalize
\renewcommand\tikzexternalize[1][]{\tikz:externalize[##1,mode=only graphics]}
\tikzset{%
tex4ht inc/.style={%
/pgf/images/include external/.code={%
\includegraphics[]{####1.pdf}%
}%
}%
}%
\tikzset{tex4ht inc}%
\fi%
}
\append:defI\use@@tikzlibrary{\find:externalize##1external\@nil}%
}
You can then simplify your document:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize
\tikzset{pdf export/.style={
/pgf/images/external info,
/pgf/images/include external/.code={%
\includegraphics{##1.pdf}
},
},
pdf export,
}
\begin{document}
\begin{tikzpicture}
\draw (0,0) -- (0,1) -- (1,1) -- (1,0) -- (0,0);
\end{tikzpicture}
\end{document}
And this is the result:
