Now I think I see what you are saying. People have suggested that Lemmy needs a separate protocol to connect with other Lemmy instances to more efficiently synchronize. Gossipsub could do that. It would also be nice if each Lemmy instance only needed to keep a minimal amount of data at any one time to service the clients that connect to it while the rest exists in the swarm.

I still don’t think that you would want a phone to function as your server and your client, though. All that coordinating takes bandwidth and processing power. Phones are ill-equipped for that. Also, usually to p2p effectively you need to be able to make direct connections through firewalls. Opening your phone directly to the Internet would be a bad idea, plus I doubt any phone companies would let you do that. Without a direct connection, you would need to proxy your connection through some server somewhere and deal with bandwidth costs. Might as well just connect to a server as a client.

Maybe the final solution is software like Lemmy running with decentralized identities via the Nostr protocol that is federated out using Gossipsub.

For what it is worth, I looked to see if anyone had done Nostr over Gossipsub and I came across a project called Gossip. Looks like they are trying to use the Nostr protocol in a psuedo-gossipsub way. That coupled with the proposed Nostr NIP 72 which would allow Lemmy-like communities could make this the solution you were looking for. Obviously these are in their infancy, but it may be an idea to follow.