Google Authenticator is a bad 2FA app. Authenticator+ costs a couple of bucks but has many features that make it much easier to use, including the ability to back up an encrypted copy of your 2FA keys (standard disclaimers about risk of compromise to this file, yadda yadda yadda). When you change phones, you just download that, decrypt, and pick up where you left off; no hassle trying to replace the 2FA generators, which is a PITA when you have one 2FA, let alone going through that process for several accounts.

If you're going to use Google Authenticator anyway, at least unlock your bootloader before you initialize the identities. You can't get to the key database without being rooted, even if you're doing a full backup with adb, and unlocking/relocking the bootloader wipes the device.