I have just downloaded the new google authenticator to confirm what is on the news:
The danger with Google’s new cloud backup for 2FA authenticatorGoogle is no more only close source 2FA, it is now doing code backup on the google online cloud. It gives convenience, but there are many people that have lost their coins, or their wallet hacked because of online cloud issue. Backup your 2FA codes offline is better and be careful not to lose it.
The 2FA app that I can still tell people to use is Aegis.
If you do not want online cloud, do not update to the latest google 2FA. If you update it, I believe you have your email already on your phone, that is only what it would be required and that will be when you will know that it is too late.