I worked on a p2p group chat app for a short time (no central server, same as this), but the group updates were a real problem. how do they get distributed?

The group creator distributes the updates to each group member individually (each pair of users has their own buckets). Of course, if the member is not online for a long time, the update does not just get lost, it gets republished and will continue to republish until the member has read the update. Did I answer your question?