last time I checked (two years ago), Google Authenticator made it horribly complicated to export TOTPs managed by it.
It took me an evening and many unsuccessful attempts to get my 10 or so Google Authenticator-managed TOTPs in a format that I was able to import into other open source solutions (eg Authy Authenticator Android app, KeePassX Linux application).
I don't care if things have changed, it was a shit experience. I highly suggest to stay away from the Google Authenticator lock-in danger.
Google Authenticator, like the Microsoft Authenticator, goes beyond mere TOTP and if you use that (or it's required by Google) then you need an app that can receive a push notification as part of the 2FA. This is the part that would screw up a lot of the consulting work I'm doing with client Google accounts because it would mean getting a separate installed instance of Google Authenticator for each account.
The point of my rant was that with modern day Google, TOTP authentication is not enough.