>>Would it work to ask the administrator to disable my 2FA, and enable it back?
Is this a Work or School account? Awesome - I assumed that you were talking about a personal MSA, haha. This explains why you can't get a code via SMS either.
Please reach out to the admin to reset your two-factor authentication (2FA), which will allow you to reconfigure it. In the future, make sure to back up your configuration to the cloud to prevent this issue from happening again. :)