If you're interested in moving away from Google Auth, look into a password manager for added security. Along with storing passwords, managers like 1password support 2FA and store your information in the cloud using a Zero Knowledge model. I've been using it for a few years and have not had any reason to use Google Auth.
I'm an active subscriber of their service and have had no issues. The results are good, very rarely do I query through Google anymore.
If you're interested in moving away from Google Auth, look into a password manager for added security. Along with storing passwords, managers like 1password support 2FA and store your information in the cloud using a Zero Knowledge model. I've been using it for a few years and have not had any reason to use Google Auth.