At some point social networks had XMTP servers, so it was possible for users to chat across social networks as protocol supports federation. It was even possible to use iMessage as a client.

Sadly, XMTP died once platforms gained enough users. The protocol itself is quite complex because of custom extensions (XEP) and different clients supporting different set of extensions.

I wasn't able to find a good desktop/mobile experience where I looked into self-hosting the XMTP server.

I think you are conflating XMTP with XMPP. XMTP is some new-ish blockchain bullshit. XMPP is the old messaging protocol.

Why bs