New Messenger connection not working

Today Beeper (latest version, I‘ve checked) on iOS showed me Messenger is disconnected and requires to reconnect. On reconnecting it shows brand new login screen directly from Beeper (it used to be Messenger login in iframe), but when I enter the FB credentials, it shows me almost immediately invalid credentials error. I know the credentials are correct (they are from keychain) because in FB app it shows 2FA approval. But even if i approve it, the login is still just failed, it doesn’t wait for the 2FA approval. I’m stuck in this. Any advice except turn off 2FA which I don’t want to?