Earlier quoted context omitted.
As long as you use encrypted backups with iPhone, your GA keys are backed up and you can restore a new phone with them also.
Last time I did a backup/restore between iphones using encrypted itunes usb, GA came up empty. Had to go through painful account recovery / lost 2fa procedures on a dozen accounts. Now I use "OTPAuth" instead. Even comes with an Apple Watch app!
I also switched to OTPAuth, great app, provides encrypted backups and switching to a new phone was seamless. Would absolutely recommend over Google Authenticator.