Tl;Dr: Beeper has rolled out a new app, Beeper Mini, just for iMessage. It claims that the new app is a privacy improvement over the standard Beeper app (now called "Beeper Cloud")
The claims:
All messages are end-to-end encrypted before being sent. Beeper (and Apple) cannot see your messages.
Encryption keys never leave your device.
Beeper Mini connects directly to Apple servers. There is no Mac server relay, like other apps.
No Apple ID is required. Beeper does not have access to your Apple account.
Your contact list never leaves your device.
In another post, Beeper says they plan to add Signal to Beeper Mini.
I currently use Beeper, but I do not give it access to my Signal messages.
If these new claims about Beeper Mini are true, though, and if Signal is ever supported in Beeper Mini.... I might actually consider bringing it in. I would love to have fewer chat apps!