You're in luck: Some people already thought of this, submitted an RFC to the IETF and implemented it. It goes by the name XMPP.

XMPP is terrible though. To be fair so is email. And activitypub. Maybe federation is just terrible.

Many earth rotations ago, I was IMing through an mIRC bot because I refused to install MSN. This kind of reminds me of that too.

I used Bitlbee until not that many earth rotations ago - it's an IRC daemon that provides bridging of various other chat protocols. It worked way better than you would expect, especially back in the day when you could use XMPP to connect to the various proprietary chat services.

I didn't stop using it until I stopped caring about those chat services.

These days I run a Matrix home server with bridges to Slack and WhatsApp so I can use fewer chat clients.

I do wish the Matrix client situation was less messy.