Sort of. That is the dream. An OS that acts as a signing service and p2p network manager. My personal project for the last 6 years has been something nostr-ish that has those goals. I can't jump straight to an OS though. Instead I am very slowly working on a webassembly VM that exposes the signing, encryption, storage, and comms layer to applications running on it.
It isn't nostr though. I like to do premature optimization and use faster cryptographic primitives. :-p ed25519, blake3, byte strings instead of Json.
All wonderful in theory, very slow development pace.