`xsltproc --html` is an example of HTML input (probably HTML4 parsing rules though?) if you really need it. This is an XSLT 1.0 processor, wrapping libxslt which most browsers use.

As for output, the difference is largely irrelevant for browser purposes since they just want a tree.

I'm not sure how many extensions the browsers allow, but a major part of the reason XSLT 2/3 failed to take off is because libxslt already provides most of the useful features from newer versions as extensions (many via EXSLT-namespaced modules, at least partially supported in browsers - see MDN); what it doesn't do is implement the unnecessary complexity that the Java world loves.