Is there any loss of privacy while using 2 Factor authentication?
If you use Google Authenticator on an android phone (where essentially you have linked your google id), to authenticate the login of a third party website, can google link your google id with the credentials of the third party website?
Google authenticator is very safe to use. You can use it even if your phone is not connected to the internet. It isone of the most used application to tighten the security of your account. I enabled all of the two factor authentication of my crypto related accounts. I highly recommend Google Authenticator for your 2FA.