Anyone who owns a server can access all the data stored on it, unless the data is end-to-end encrypted. Whether it’s mastodon, Lemmy, Facebook, twitter, Gmail, vBulletin, whatever.
If you need to say something that you can’t risk anyone else seeing, use an end-to-end encrypted messaging app, or implement encryption yourself using e.g. PGP.
I don’t think we’re heading towards an everything app, but we may well see an everything account at some point. Companies already use social media management portals to post/respond on multiple platforms; I think if that kind of commercial demand arises for fediverse services, we will probably see similar fediverse management portals which allow you to interact with content on multiple ActivityPub services in a context-sensitive way via one account.