Tabularray should work, hopefully.

Thanks for the report. This package seems to be huge, so it will be not easy to fully support it. We need to patch the right commands to insert the HTML or XML tags. I've already found which commands insert table rows and cells, but the support for merged cells and rows, various styles of rules, and colors, will be more complicated.

Here is a basic configuration file, tabularray.4ht:

%%%%%%%%%%%%%%%%%%%%%%%%
\NewConfigure{tabularraycell}{2}
\NewConfigure{tabularrayrow}{2}

% disable rules
\special{t4ht@_}
\ExplSyntaxOn

\def\:tempa#1{\a:tabularrayrow\o:__tblr_build_row:N:{#1}\b:tabularrayrow }
\HLet\__tblr_build_row:N\:tempa

\def\:tempa#1#2{\a:tabularraycell\o:__tblr_build_cell:NN:{#1}{#2}\b:tabularraycell}
\HLet\__tblr_build_cell:NN\:tempa

\ExplSyntaxOff

% configure tags
\ConfigureEnv{tblr}
{\ifvmode\IgnorePar\fi\EndP\HCode{<table>}}
{\ifvmode\IgnorePar\fi\EndP\HCode{</table>}}{}{}
\Configure{tabularrayrow}{\HCode{<tr>}}{\HCode{</tr>}}
\Configure{tabularraycell}{\HCode{<td>}}{\HCode{</td>}}
%%%%%%%%%%%%%%%%%%%%%%%%%%

It just puts cells and rows to the correct HTML tags, nothing more. It cannot detect merged cells and rows, or any fancy rules. I will take try to create something more serious next week, hopefully.