As a fellow introvert, I’ve found that being meek and timid about uncomfortable situations just invites more trouble from extroverts. The best way to handle it is to be direct and firm. If she wants to be nosy, then drop all the gory details:
"I’m an introvert and I don’t feel comfortable sharing my personal life with coworkers. I know you, as an extrovert, want to be involved in everyone’s personal lives and there’s nothing wrong with that, but as a leader and a manager, you need to understand how to change tracks and adapt to your subordinates’ needs.
“I need time to myself to recharge; being around people is mentally and emotionally draining for me. It’s not something I can “fix,” it’s just the way I am, and no amount of exposure to people or social events will ever change that. I need you to understand that and adapt to my needs, in order for you to effectively manage me.”
I worked my way up the ranks in the US military and eventually found myself managing people. As an introvert, I found it extremely difficult to get out and talk to my subordinates. But I soon realized that the mission wouldn’t get done unless I did my job, so I quickly learned how to fake an extroverted personality while at work so I could talk to people and ensure mission success. Then I’d go home and crash. I’d spend my evenings either sleeping or bundled up, watching TV or playing video games, just to recharge so I could do it all again the next day.
But one of the things I learned was how to adapt to the needs of my subordinates. I had one guy who was a complete fuck-up. Couldn’t do anything right without someone holding his hand. So I either had to be very hands-on with him, or delegate that responsibility to one of my subordinate leaders.
But then I had another guy who grew up in a ghetto being plagued by corrupt cops, and he hated anyone in an authority position over him. Why he joined the military, I dunno. We were all about authority and respecting rank and file. But if I even spoke to him, he would shut down and then be unproductive all day. As long as I left him alone, he was my hardest and most productive worker. So I learned to leave him alone and he practically did my job for me. Maybe your supervisor needs to learn that lesson with you.
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.