Yeah, this is a fair distinction. I think the issue is what qualifies as hate speech nowadays. Some people think that saying a woman is an adult human female is hate speech. Others think it's fine to call for the murder of people they disagree with on a whole range of subjects. As long as the people they disagree with are on the "wrong side" of course.
Musk has already said he thinks the standards of censorship should reflect the law but not significantly exceed it. I think that's a pretty good standard. No threats of, or incitement to, violence. But I think most of the people framing free speech as the coming apocalypse are really just taking about mean names or differing opinions.
Yeah, the "truth" part is the most difficult part of social media in general. Having anybody be the arbiter of what's true is such a terrifyingly slippery slope that I must admit I really struggle to ban what appear to be lies in all but the most absolutely egregious cases (Trump's election lie qualifies for me here).
I don't see the authenitacion thing as a real problem though. People are already frequently doxxed on social media. It's sadly not that difficult if somebody really wants to do it in our oversharing world. The benefits would be to make bot accounts harder and to create a little accountability. You'd still be able to post under a pseudonym, your real name wouldn't need to be public facing, just accessible by Twitter. I mean, if you're saying somehing you genuinely wouldn't want to be associated with you, perhaps you shouldn't be saying it, no?