Is it possible to use different a `indentUnit` for each language?

I want to use tabs for indentation in Markdown, and spaces for indentation in everything else. I found the indentUnit facet/extension, but that seems to be universal and so I’m struggling to figure out if it’s possible to scope the indent unit per language.

Yes, indentUnit is set per-document. You may be able to bind a custom command to enter that, when in markdown context, does some kind of tab-based indentation.