Nostr

Maybe you didn’t realize but if you go to any client and log in with someone else’s npub1 key you will see the feed as they see it

Yes. That's one cool thing about Nostr. You can experiment the following list of another person (and check who is he having DMs with!)

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Second part is not that great.

Check who they are DMing, but not see what those DMs are right? Reading the DMs requires the private key right?

Yep

Correct!