It’s more about framing the conversation in a way that helps OP’s supervisor realize they’re at odds with each other, socially, and that the supervisor needs to make changes, not OP. I know it’s a bit blunt and direct and may not exactly describe their relationship, but I’ve found that being direct and binary with extroverted people generally gets them to the point faster, rather than beating around the bush with complex descriptions of their dynamic.
And the supervisor being an extrovert is definitely a part of the problem in this case. They’re ignoring signals from OP that they don’t want to be social, shaming them for it, and forcing public interactions in order to change them. This is classic extrovert behavior which is making OP uncomfortable.
The topic of discussion is definitely off-limits and deserves a conversation with HR, but the supervisor still needs to understand that OP’s antisocial behavior isn’t a problem. Otherwise, the discussion will change to be more work-appropriate, but the behavior will remain.
When I lived in Germany for a couple years, I was surprised to learn that the large church in the center on my village was about 1,000 years old. This one building has been standing longer than America has been a country. Over 4x as long, too! European culture amazes me because there’s such a lengthy history, and so many things are much older than I’d imagine. American history is so short in comparison, and we’re more likely to tear down and build new and cheap than create a solid structure that will last for hundreds of years.