T59886 handled the case where the special page transclusion was at the top level. The solution there doesn't work if the special page transclusion is nested in a template, as the commit message says,
As a first pass, we call out to the legacy parser for the output of
special pages, which is HTML ($isHTML in Parser.php) and only returned
if asked to render ($this->ot['html'] in Parser.php) as opposed to
template expansion ($this->ot['pre']).
I suggested to @Arlolra that this could be solved by integrating strip state into the parsoid tokenizer. Parsoid expects the result of a transclusion to be "wikitext" and the result of an extension tag expansion to be "html". Both of those are actually incorrect: transclusions (including parser functions) can result in html (returning ["some html string", "isHtml"] as documented by Parser::setFunctionHook) and extension tag expansions can result in wikitext (returning [ 0=>"some html string", "markerType"=>"none"] when called from Parser::extensionSubstitution()).
The solution used in the core parser is to encapsulate the HTML in a strip state marker. Parsoid could integrate "strip state marker" as a token type in its tokenizer, and then use that to fetch the raw html from the strip state and encapsulate it into a DOM Fragment token. That would allow any combination of HTML and wikitext to be handled properly by Parsoid.
This is elaborated on in T257606#9216083.