Checked again. Beeper will be running “local bridges”. Once these are implemented into a modular system, there is not really a need for a local chat protocol in my understanding. The matrix connection can simply become another bridge and a Beeper server for Beeper chats would basically be yet another matrix server.
https://blog.beeper.com/2024/06/04/2024-beeper-roadmap/?ref=textscom
Using it for years and am fully satisfied. Basically, any imap client capable of encryption will do.