If you prefer not to give your phone number to Google, don't. Just turn on two-factor auth using a non phone number-based auth method, either the Authenticator app or (better yet) a security key, or both. Then download and print out some backup 2FA codes and keep them somewhere safe. Google won't have your phone number and you won't be vulnerable to mistakes by dumb telco customer service reps.
Not google, but on Twitter I've had to use 2FA codes 2-3 times daily - any hiccup, and I have to log in again, and every time(!) it'll request a code.
Sure, could print a dozen or 2, but I'll burn through them quickly.