Has anyone looked into the Nostr protocol at all? I wonder how it compares to ActivityPub?

I guess the biggest difference for users is that nostr relays don't federate with one another. So you'll have to query multiple relays yourself if you want to see stuff outside of the relay(s) you post to. The other big difference is that your identity is a keypair. The relays you send to only know your public key and that's it.

E: someone running a relay could still decide you need to create an account or something, but this account is only the permission to use this specific relay. Your identity would still be your keypair, so moving to another relay is easy.