Microblogging shouldn't have private messages. Let people have a profile and a link to an email address or similar and be done with it.
I'm not sure why a service designed to publicize things so that everyone can see them ALSO chooses to take on "private messages." I get that's how the big money incumbents see it, but I feel like less would be more here.
I have absolutely no confidence in any e2ee implementation that would be served from twitter.com and trusting Elon or anyone that still claims to speak for Twitter on any security guarantees it offers would be foolish. They also recently broke the API for their "circle tweets" which is supposed to let you create private tweets that only go out to a subset to your followers, and stay private to everyone else, but of course that ended up not working anymore and they ended up in your profile.
There is nothing stopping this from being implemented in ActivityPub too, and in fact there are already pub/pri keys there to do this. However you still need to trust that the instance you are on and the one your are communicating with play by the rules.