You're touching on a matter that I wanted to investigate myself as soon as possible. Even though I stopped using the Google Authenticator for accounts that say that online this one is supported I found that the Microsoft Authenticator app can as well import these keys. So I'm using the Microsoft Authenticator app for all accounts that have 2 factor security enabled.

That being said, I am not sure how I will get all keys back if I need to replace my iPhone. I'm hoping that everything set up in the Microsoft Authenticator app get's synced through iCloud. If that's the case then I'm pretty much all set. If that is not the case and I won't get the app back as I last synced it, then I will definitely need to start exploring other possibilities. Authy seems to be a pretty good solution but I'm hesitant of their own cloud backup nonetheless.

EDIT: did the research immediately and this is what came up:

• I restored my device from a backup, and my account codes are missing or not working. What happened?

For security purposes, we don't restore accounts from app backups. After you restore the app, delete your accounts and add them again.

• I got a new device. How do I remove the Microsoft Authenticator app from my old device and move to the new one?

Adding the Microsoft Authenticator app to a new device does not automatically remove it from any other devices. To manage which devices are configured for your account, visit the same website that you use to manage two-step verification, and choose to remove old apps.

So I definitely need to figure out what to use to prevent this from happening. Will look into Authy a bit more.