#enumeratemake4httex4ht
The enumerate package causes problems with make4ht, there are extra spaces and strange alignment.
\documentclass{article}
\usepackage{enumerate}
\begin{document}
\begin{enumerate}
\item text
\item other text
\end{enumerate}
\end{document}
I compile with make4ht file.tex
Regarding your caption problem. I don't get any error. I would suspect that your caption.sty is too old.
I have caption.sty 2010/01/09 v3.1m Customizing captions (AR)
Use the widestkey for that:
\documentclass{article}
\usepackage{lipsum}
\usepackage{enumitem}
% Section numbers and enumerate numbers are not left aligned, however the indentation of text is constant (how I want it)
% \setenumerate[1]{label=\thesection.\arabic*,labelwidth=1.5cm,labelindent=10pt,leftmargin=1.2cm}
% Section numbers and enumerate numbers are left aligned, however the indentation of the text is not constant
\setenumerate[1]{label=\thesection.\arabic*,labelsep*=12pt, widest=00.00, align=left, leftmargin=*}
\setenumerate[2]{label=(\alph*), ref=\theenumi{} (\alph*), align=left}
\begin{document}
\section{Test}
\begin{enumerate}
\item \lipsum[2]
\end{enumerate}
\setcounter{section}{22}
\section{Double digits}
\begin{enumerate}
\item \lipsum[2]
\setcounter{enumi}{21}
\item \lipsum[2]
\begin{enumerate}
\item \lipsum[2] % The (a) should be aligned with the text in the item above
\end{enumerate}
\end{enumerate}
\end{document}
Best Answer
It seems that there is a large space between the enumerate label and text. You can remove it using the following config file:
It uses a CSS code that sets the left margin of enumerate text to zero, which removes the large space.
This is the result: