Sadly it is not possible, but yea, beeper host their own matrix server which is the only server the client connects to. At least we can use all the bridges with our own matrix server.

Edit: lol, that photo quality 🥲 it is a mail conversation with beeper:

Me: I have a matrix homeserver and want to use beeper client with it, is that possible?

Beeper: That is not possible at the moment.

Me: Oh, what a bummer… But thank you very much for the fast reply! Is it planned that the client will work with selfhosted servers in the future, or is is it possible to selfhost a beeper-matrix-server?

Beeper: No plans for it at the moment. And negative.

So sad…