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I've fixed most issues, such as the \Link command defined by both TeX4ht and Xyling or extra tags and missing references for tcolorbox environments. Some of these fixes are already available in TeX Live or should be available in a few days.
A configuration file named logic2.4ht can fix other project-specific issues for your class. This file should be loaded automatically if you place it in the directory with your sources:
\RequirePackage{etoolbox}
\renewcommand\doclicenseThis{\ifvmode\IgnorePar\fi\EndP\HCode{<p >This work is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/?ref=chooser-v1" target="_blank" rel="license noopener noreferrer" style="display:inline-block;">CC BY-NC-SA 4.0<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/cc.svg?ref=chooser-v1" alt=""><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/by.svg?ref=chooser-v1" alt=""><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nc.svg?ref=chooser-v1" alt=""><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/sa.svg?ref=chooser-v1" alt=""></a></p> }}
\renewcommand{\wlabel}[2]{\Kk[#1]{0}{\ifstrequal {#2} {} {} {\ensuremath{(#2)}}}}
\AtBeginDocument{
% fix for the extra </div> after the proof environment
\Configure{proof}{}{}{}
}From these definitions, only \wlabel is critical, as it fixes the fatal error caused by \ifthenelse. I couldn't find the source of this issue. \Configure{proof} prevents extra closing </div> tag after the proof environment. You can remove the redefinition of \doclicense if you fix it differently in your Python script.
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