No, it's not. I don't get the 2FA code. It never worked before for me. Never worked with Beeper proper either.
Do you get 2FA codes when logging in from am actual Apple device? Because it might be an issue with how your apple account is set up to do 2FA that has nothing to do with beeper
In the past, I tried creating an app password as well, but it didn't work either. Now, it fails to create an app password, but you still can't log in with an app password.