Even if you run your own instance, like I do, you have no #privacy on the #fediverse.

Only I get to read the direct messages received at my instance but I have no control over who sees the direct messages I send to other instances.

So, again, until end-to-end encryption is mandated by the core protocol (ActivityPub), remember:

Treat all posts on #mastodon / the fediverse as public and use an end-to-end encrypted messaging app like Signal if you want to have private conversations with people.