Strange vertical spacing in tcolorbox after center

Question

This is a sequel to this question, which was partially resolved and it was suggested there that I start a new question.

I've created a box with tcolorbox, which should not float and I want to attach a caption which should "stick" in the sense that it should be on the same page as the box.

The solution suggested by Zarko in my previous question does strange things to vertical spacing inside the box, as can be seen in the code below.

I came up with a small workaround in the previous question but the caption doesn't stick. Does anyone have any suggestions for a workaround or fix?

\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{babel}
\usepackage[skip=1ex]{caption}

\usepackage{tcolorbox}
\tcbuselibrary{most}
\newtcolorbox{abox}[2][]{enhanced, fonttitle=\bfseries, 
                         attach boxed title to top center={yshift=-2mm}, 
                         title={#2},#1}

\usepackage[unicode=true,
            pdfusetitle,
            bookmarks=true,
            bookmarksnumbered=false,
            bookmarksopen=false,
            breaklinks=false,
            pdfborder={0 0 1},
            backref=false,
            colorlinks=false]{hyperref}

\begin{document}

\begin{center}

\begin{abox}{title}
{
{\begin{enumerate}
\item testttttt 
\end{enumerate}
testttttt
\begin{enumerate}\setcounter{enumi}{1} 
    \item testttttt
\end{enumerate}
testttttt
\begin{enumerate}\setcounter{enumi}{2} 
    \item testttttt
\end{enumerate}}
}
\end{abox}
\captionof{figure}{caption}

\end{center}

\end{document}

Answer 1

I am not sure about certain items in your example, so I changed some of it to be able to target the lack of vertical spacing at the first enumerate. This code example shows the correct vertical spacing inside and outside the tcolorbox:

\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\usepackage{babel}
\usepackage[skip=1ex]{caption}

\usepackage[most]{tcolorbox}

\newtcolorbox{abox}[1][]{enhanced, fonttitle=\bfseries,
    nofloat,    % added to prevent tcolorbox becoming a float
    attach boxed title to top center={yshift=-2mm}, 
    title=#1}

\usepackage{enumitem} % added to use the resume option

\usepackage{lipsum} % just to insert some random text

\begin{document}
    
    \lipsum[1][1-2]
    
        \begin{abox}[title]
            top text
                \begin{enumerate}[leftmargin=*]
                        \item testttttt 
                \end{enumerate}
            
                    testttttt
            
                \begin{enumerate}[resume*]%\setcounter{enumi}{1} 
                    \item testttttt
                \end{enumerate}
                
                    testttttt
                
                \begin{enumerate}[resume*]%\setcounter{enumi}{2} 
                    \item testttttt
                \end{enumerate}
                    testttttt
        \end{abox}
        \captionof{figure}{caption}
    
    \medskip    
    \lipsum[2][1-2]
    
\end{document}

I made the following changes:

1. added the enumitem package, so you can use the resume* option in subsequent enumerate occurrences without having to reset the counter
2. changed the number of variables in your abox to just one for the title. You don't need to define a variable for the content of the box
3. removed all superfluous brackets as a result of that change
4. added the option nofloat to your box definition as you clearly stated you don't want the box to be a floating object
5. removed the center environment as that is no longer required to prevent floating
6. since the caption is following the box, but not attached to it, you need to add some vertical space to increase the distance between caption and next paragraph. You can't use the option before / after skip balanced from tcolorbox (see pages 86-88 in the manual)

The result of these changes:

As to why the vertical spacing is altered at the first enumerate when embedded in a center environment, I have no clue.

Edited to include options in comments

\documentclass[english]{article}
%\usepackage[T1]{fontenc}
%\usepackage[latin9]{inputenc}
\usepackage{babel}
\usepackage[skip=1ex]{caption}

\usepackage[most]{tcolorbox}

\newtcolorbox{abox}[1][]{enhanced, fonttitle=\bfseries,
    nofloat,    % added to prevent tcolorbox becoming a float
    attach boxed title to top center={yshift=-2mm}, 
    title=#1}

\usepackage{enumitem} % added to use the resume option

\usepackage{lipsum} % just to insert some random text

\begin{document}
    
    \lipsum[1][1-2]
    
        \begin{abox}[title]
            caption inside a parbox
                \begin{enumerate}[leftmargin=*]
                        \item testttttt 
                \end{enumerate}
            
                    testttttt
            
                \begin{enumerate}[resume*]%\setcounter{enumi}{1} 
                    \item testttttt
                \end{enumerate}
                
                    testttttt
                
                \begin{enumerate}[resume*]%\setcounter{enumi}{2} 
                    \item testttttt
                \end{enumerate}
                    testttttt
        \end{abox}
        \noindent \parbox{\linewidth}{\captionof{figure}{caption}}
    
    \medskip    
    \lipsum[2][1-2]
    
    \noindent \begin{minipage}{\linewidth}
    
            \begin{abox}[title]
        boxed inside a minipage
        \begin{enumerate}[leftmargin=*]
            \item testttttt 
        \end{enumerate}
        
        testttttt
        
        \begin{enumerate}[resume*]%\setcounter{enumi}{1} 
            \item testttttt
        \end{enumerate}
        
        testttttt
        
        \begin{enumerate}[resume*]%\setcounter{enumi}{2} 
            \item testttttt
        \end{enumerate}
        testttttt
    \end{abox}
    \captionof{figure}{caption}
    \end{minipage}
    
    \medskip
    \lipsum[4][4-8]
    
\end{document}

This code example shows the correct indention after the use of \captionof: