Brad Murray has confirmed that all bridges will migrate away from being Matrix Appservices (“cloud bridges”), although the option to self-host your own version of beeper’s Appservices will remain an option

Brad Murray The current plan is for each client to send and receive with their own locally running connections, as opposed to letting one client use another client’s connections to send in real time. We’ve had some pretty bad experiences with the old androidsms bridge with that architecture (since only your Android phone could send or receive a SMS).

Brad Murray We’re still going to keep all our bridges open source and usable as Matrix Appservices, so if you want to use any Matrix client it’s probably best to self-host against Beeper’s homeserver (which we’ll still support) or just run your own homeserver with our open source bridges