When sending and receiving Signal, iMessage and WhatsApp messages, Beeper's web service acts as a relay. For example, if you send a message from Beeper to a friend on WhatsApp, the message is encrypted on your Beeper client, sent to the Beeper web service, which decrypts and re-encrypts the message with WhatsApp's proprietary encryption protocol.
I don't know how tech savy you are but I selfhost Matrix and almost exclusively use bridges to talk with friends. I feel comfortable breaking e2e on a system I control and the all-in-one-place messaging is pretty sweet, like Pidgin used to be.
If you are already comfortable self-hosting other services, Matrix doesn't really impose any additional complexity IMO and the bridges I use seem to be very stable.