Ok, so I've introduced a new configuration for early package patches. As testing for file existence is too slow, it will need to be declared in usepackage.4ht. So it isn't as flexible as the way I tried with the <packgename>-sty-hooks.4ht file, but it is faster and easier to write than the old way.

To introduce the early package hooks, you can now write the following code in tex4ht-4ht.tex:

\<add to usepackage\><<<
\Configure{PackageHooks}{packagename.sty}{packagename-hooks.4ht}

>>>

\<packagename-hooks.4ht\><<<
% code that fixes the package loading

>>> \AddFile{9}{packagename-hooks}

The unbalanced quote message is not coming fromtex4ht. As far as I can tell, it comes from l3file.dtx (texmf-dist/source/latex/l3kernel), around line 2486 (at the moment):

\cs_new:Npn \__kernel_file_name_strip_quotes:nnn #1#2#3
{
\int_if_even:nT {#2}
{
\__kernel_msg_expandable_error:nnn
{ kernel } { unbalanced-quote-in-filename } {#1}

l3kernel is included in the LaTeX(2e).fmt files now.

By the way, even if LaTeX didn't check, the binaries would report the error (web2c/lib/texmfmp.c, function normalize_quotes). Quotes have to be balanced in filenames for security reasons, otherwise the quoting of special characters (so filenames like "|`rm -rf /`" don't actually run anything) might get defeated.

I've got a strange error after recent LaTeX update. TeX4ht produces errors when the Minted package is used:

\documentclass{article}
\usepackage{minted}
\begin{document}
hello world
\end{document}

You can compile this document using:

make4ht -sm draft filename.tex

It produces the following errors:

[ERROR] htlatex: ./tex4ht.sty 4603 Undefined control sequence.
[ERROR] htlatex: ./tex4ht.sty 4603 Undefined control sequence.
[ERROR] htlatex: ./tex4ht.sty 4603 Undefined control sequence.
[ERROR] htlatex: /usr/local/texlive/2020/texmf-dist/tex/latex/xcolor/xcolor.sty 1455 Missing number, treated as zero.
[ERROR] htlatex: /usr/local/texlive/2020/texmf-dist/tex/latex/xcolor/xcolor.sty 1455 LaTeX Error: Missing \begin{document} in `'.

When I compile it in the debug mode, I get some more info:

<argument> LaTeX3 error:
Unbalanced quotes in file name '"filename.4ht'.

I guess that it is somehow related to the LaTeX kernel update :(