https://security.googleblog.com/2023/04/google-authenticator...

Google Authenticator can be local-only or synced to the cloud.

In local-only mode, the authenticator is bound to a specific device. You can manually sync it to additional devices, but if you lose access to all those devices, it's game over, you will get locked out of whatever accounts you secured with authenticator as the second factor.

In cloud-synced mode, it's synced to your google account, so if you lose your phone, you can restore authenticator state. But if your google account gets taken over, it's game over, the attacker has your authentication codes.