Is there a way to opt out of this? If I installed Authenticator on my Android phone, would it immediately and gratuitously sync everything to my account? Can I

Is there a way to opt out of this? If I installed Authenticator on my Android phone, would it immediately and gratuitously sync everything to my account? Can I log out and stay logged out on the app so that it never syncs? If someone uses Chrome's password manager and Authenticator's TOTP, this seems to make account takeovers an exceptionally juicy prize. Capture a Google account and you've captured credentials and all necessary factors in one fell swoop. Well done, bravo. I mean, account takeover already means game over because you can read/send email, but the whole idea of device-based TOTP is to isolate it from anything with an attack surface.