I have several 2-step verification options in the account, including Authenticator and SMS. Authenticator is lost. On signing-in I can successfully use SMS, but when I try to access the 2-step verification settings in my account, Google asks for my password again and then requires me to pass the second step, where only the Authenticator is available.
Why doesn't it allow me to use SMS and how to recover access to the 2-step verification settings now?
I've read How do I turn off the Gmail 2-step verification?, but there is no “Can't access your account?” option in my case. Moreover, the difference is that I can sign in with another step.