Just your average Reddit refugee.
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.
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.
Then the p2p network is really the “server” and the phone is still just a client. I’m also not sure that a p2p network could be queried very well because something would have to be able to produce aggregated and sorted results. It isn’t like pulling one file from a swarm. It would be like a blockchain and the phone would have to download the whole dataset from the p2p network before running queries on it.
What you are talking about sounds kind of like the Nostr protocol. It is a distributed social network trying to solve the same problem that ActivityPub is but in a slightly different way. All the events are cached on multiple relays and the client applications query those relays looking for information that gets aggregated and sorted on the client however it wants.
ActivityPub is all about pushing content around to subscribing servers. It sort of expects the subscribers to always be online which would not work for a phone. Servers could resend missed events, but essentially you would miss every event that occurs while the phone is asleep or doesn’t have the app running.
Also, every event that occurs needs to be processed and stored whether or not you are actively looking at it so it would be a huge battery drain while it was running.
It is definitely a service best run on an always-on server with a client application in a phone just asking the server for the latest stuff on-demand.
Reddit is an example of a Group system where posts are associated with a group. This is the model Lemmy uses.
Twitter is an example of a Person system where posts are associated with a person. This is the model Mastodon uses.
Some services can do both; like Kbin with their microblogs and magazines.
Sounds like the Wordpress implementation uses the Person system that Lemmy does not support at the moment, but probably works on Mastodon and Kbin (idk for sure).