You've got it! You run a P2P system on your local machine... in theory, you don't need the internet to communicate. Messages can be sent via your friends hopping between LANs using the underlying gossip protocol.

it's like federation, but at the level of a user. Much easier to set up, much easier to curate / moderate what you want to see. There's still emergent community in the space, it's just not tied to the politics of hardware

I wouldn't say it's "like federation" at all. In no scenario do you have an entire group of people who suddenly loose their accounts and connections if the owner of the "server" they connect to decides to stop hosting it (as has happened with many mastodon instances).

In addition in works offline (including images). Many of us catch up with friends and reply to their posts when on the train, plain, boat, road, whatever and sync up when we get to a net connection, or local connection to a local friend with SSB.

> it's just not tied to the politics of hardware

What do you mean by this? Is there some sort of hardware politics battle in the GNU social community or something?

When someone else runs the server you use, and your account is tied to their server, you are at the whims of the server owner, and are not able to migrate your identity.