This is why even if you are making encrypted backups of your phone, which Apple claims are full backups that store passwords and everything, your Google Authenticator data will be completely gone when you restore. So if you thought that, for example, there would be no reason to store the 16 digit codes 2FA codes as long as you had a multiple backups of your phone, what happens is that you just get locked out of every single website you use for a month.
It also means that if an app is no longer in the app store, there is no way to get that app back even if it would otherwise still work on your phone.
If you look at the text of how the backup process is described in iTunes, they are clearly claiming that a full backup of the phone is getting made, and yet in reality nothing could be further from the truth. It's amazing there aren't multiple billion-dollar class action lawsuits currently pending on this issue.