I'm sorry, but that's not an answer. WhatsApp encrypts the message E2E, and then Beeper is bridging it into Matrix. The only way this would make any sense is if they've bridged E2E all the way through to ... the clients? Like, it doesn't make any sense.
They actually reverse engineered Apple's iMessage and released a POC. At the time it worked and demonstrated on device bridges being a possibility. The runs locally and then encrypts it client side before it reaches beeper services. This can be enabled for Signal under experimental settings already.
Well, now I regret that this comment sounds a bit dismissive, if another reply is true and they run the bridge locally. That's... impressive, and still surprising to think about.
I'd honestly be fine with accepting the compromise of hosted bridges, especially since they seem to offer the ability to self-host the bridges, while using Beepers' Matrix infra. Gives them some extra cred in my book.