This is something to do with Google Messages, as far as I'm aware. On initial installation of Google Messages - both stock and GrapheneOS I have found that QR pairing is the only kind of pairing available.
After an undetermined amount of time (or perhaps after some event that isn't clear to me? maybe a regular feature flag enabling on the google side for new users?) eventually pairing via sign-in with google is enabled on Google messages. This is - again - on both stock pixel & GraphenOS.
For your specific case: Until the option is available to you it is possible to use QR code pairing with beeper via hosting your own Google Messages bridge. The Google Messages bridge that is hosted by beeper only supports sign-in with google.