Nostr is a Twitter alternative that's decentralized, not a Reddit alternative.
Nostr is not P2P. Its a broadcast protocol. Nostr is pub/sub, distributed, decentralized; while others such as Matrix,mastodon, bluesky are federated and are somewhat closed than nostr.
No, they (Nostr) are not doing ActivityPub. ActivityPub requires server-to-server communication, which Nostr does not have. They only have client-server communication. And the actual protocol is different to ActivityPub, all the way from the transport (which uses WebSockets rather than HTTP REST) to the schemas of the objects being passed. They also rely much more heavily on public key cryptography.
Nostr takes decentralization too far to be practical for a wide audience IMO. The relay model is even more abstract than Mastodon instances (which can at least be analogized to e-mail hosts) and the public/private key system is both inaccessible (copy/paste a key or look people up in a directory-- like a phone book! Friend codes on steroids) and unforgiving (no password resets). Like much of crypto, there are interesting ideas that don't seem practical in actual use. Curious if it pans out. (https://kbin.social/search?q=nostr)