The original server operated by the Mastodon gGmbH non-profit
It will be open source, end to end encrypted using Signal’s double ratchet encryption protocol, and he plans to make it easy for fediverse platforms to integrate it. The beta will release later this month.
If they're not end to end encrypted, your messages are not actually private on any platform.
It's a bit more obvious in the Fediverse than elsewhere, as direct messages are generally stored on two separate servers (sender and receiver). Furthermore each server tends to be smaller: if Zuckerberg decides to go through people's DMs it's unlikely to affect any particular Facebook user, but if the owner of a Mastodon instance does the same it's small enough that she could actually get an overview. It's mostly a false sense of security embedded in larger services, but people are all about having a false sense of security.
Like anything, depends on the threat model. Private from your little sister? Probably. Private from your boss, at least in the next few months prior to them being leaked? Also probably. Private enough?
That's to some extent a question that can only be answered individually, as everyone's threat models differ. I suppose this fact (everyone having differing threat models) is one of the reasons that so many arguments occur over security.
In the end any successful chat service is going to be used by horny teenagers sharing nudes with each other, which is honestly for me better reason than any state secret why all communications should be end to end encrypted at all times. I don't trust Zuckerberg or Musk with that, or any other third party for that matter.
Right now I just think about me and how I'll use it. I'm eager to try this messaging app to have a way of being reachable by like-minded people.
To put it differently, I don't want to be a slave of others' choices. I know the network effect is real and that I'm powerless to break it. So I'll just change my attitude, and embrace this wave. Who knows what will happen? And in the meanwhile, I'll have fun using what to me seems right.