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.

Events could be cached on the p2p network, so the phone only pings its peers for new content (mind the existing servers would be peers on the network).

“Could be”? I mean yes almost everything is possible but you’re talking about a completely different protocol.