I've been interested in doing this, but I can't tell why I need to login to Beeper in order to self host. I noticed their previous self-host solution did not require that.
Because of that login step, I decided to look into this other repo which uses Ansible to deploy a Matrix homeserver and the same bridges that Beeper uses. I haven't finished it yet since there's a lot of config and choices to make, but it seems like it'll serve the same end goal.
Edit: lol, maybe if I read the intro, I'll get my answer.
You can connect any† standard Matrix application service to your Beeper account without having to self-host a whole Matrix homeserver.
Still might go with the second option so that I don't rely on their cloud services.