For Google, it's not a text message though, is it? IIRC, it's tied to your Google account and not to your phone number.

In what way? For its employees, it uses physical keys: https://krebsonsecurity.com/2018/07/google-security-keys-neu...

Consumer/enterprise Google accounts have supported U2F and the Google Authenticator app for quite some time. I have SMS completely eliminated as a factor on my GMail account (Yubikey primary with codes from the app as a fallback; no way to authenticate via SMS at all).

It does, and that is annoying, but you can and should turn it off.