A) install Authy on old phone, disable 2FA and enable it again on every service/login but now using Authy. When all 2FA is reenabled in Authy create a backup and then retrieve Authy backup on new phone
There is no backup option in Google authenticator
B) disable 2FA on every login you have using old phone, and reenable it later with new phone and new Google auth install (consider using Authy because it has a backup option)
IF old phone is lost/destroyed
You’ll need to contact support desk of every site, and ask them to disable 2FA on your account. Be prepared to provide info on who you are, last IP used and possible other details.
(sry @Flash didn’t see your previous answer)