Oh, I just noticed I typed "SMS 2FA". My bad! In that case, you are correct, but in my particular case I lost all data related to Google Authenticator, including the shared secret. Customer service refused to help, despite having had the same phone number, because it was not SMS-based 2FA. Sorry! I should not get on HN when so mentally exhausted. :(
We use Google Authenticator too at work, I had to go to IT in person to get a new one when I got a new phone. It makes sense to refuse to give you based on solely the phone number. However, there should be a process to renew these credentials, phones die too.
