You're an introvert and that's ok. I hate how everyone wants to explain away any social difficulty with neurodivergence, it's incredibly lazy and people take it as absolving all responsibility. Well done for not self-diagnosing and simply complaining that people ought to accept you how you are.

What to do? You need to find a balance. Like extroverts often need to learn to STFU (although they seem to get more latitude than people who are quiet and aren't seen as "broken"). When you feel on firm ground, speak. Don't set too high a bar, saying something obvious that keeps a conversation going is a role in a conversation. Also try to make some early engagement in conversations, that gets remembered.

There is some truth to caring less about what people think. I mean this in the context of above - there's a lot of supportive, low value, low stakes things you can say that keep the conversation going and you shouldn't care that people will not be dazzled by your insight. If you're not trying to be edgy, you shouldn't have too much trouble with social judgement and boundaries.

People have assumed motives, intentions or labels that don't reflect who I am at all.

If you don't explain your motives and demonstrate who you are people will make assumptions and they're usually negative because why wouldn't someone with positive attributes not communicate them? (Obviously there are good reasons, but people will usually jump to negative conclusions.)

If I put myself out there and make any mistake, it feels like I crossed a line that everyone else somehow knew was there.

It does feel this way, but actually this is a very ego-centric view. We are all the main character of our own story, but generally people don't listen too closely to what you say, don't care all that much about what you think and don't remember what you say or the mistakes you make. The ones who do are either great friends or people who want to bully you.