Nope. You own your keys, and you can switch to a different server instantly while retaining both your username and your followers. They can't impersonate you because they don't have your keys. They can't ready your messages because they don't have your keys.
It's a bit more complex underneath (e.g. the are light-clients that you can entrust with part of your key), but that's the gist.
I don't expect it to stay closed source. But there are significant differences to Mastodon. Just to give one example: Mastodon server admins actually can read your private messages. Also Blue Sky's approach to data portability and how to implement filtering/indexing is more developed. It might be personal preference, but I prefer AT Protocol's approach where the servers have less powers, and the users have more power. A lot of little design decisions add up to a qualitative difference.
Author here. You get to have all the moderation, filtering, etc. that is implemented on the servers you use.
I'm sure there will be servers that very closely try to approximate what Twitter is/has been doing. Servers also can share any and all information needed to effectively moderate.