Pseudonymous and private are different concepts. Most things you post on Nostr are inherently public, the opposite of private.
Discussion
Privacy is different from private. Privacy is basically the ability to control the level at which information is shared, sending someone a private message is nested within the concept of privacy. You can use nostr anonymously so idk why you're bring up pseudonymous. And yes, obviously a "post" is by definition public. That doesn't mean you can't use nostr privately.