Take a look at https://support.google.com/a/answer/6309862 - it may be that you've purchased workspace licenses that support Gmail, but have not assigned one of those licenses to your account.
Thankfully this has been fixed. You can now choose "Transfer accounts" (from the menu in the top right corner) to copy everything to Google Authenticator on a new (or backup) phone.
Yes, I always find it amazing how patients can have a sudden sensorineural hearing loss and wait days before presenting.
In my opinion patients and the public should treat it as urgently as a sudden sight loss.
High dose steroids are regularly prescribed in this sort of scenario in an attempt to minimize damage, and are likely to be more effective the sooner they are given.
As a Workspace customer you should also be able to contact Google Workspace support by following: https://support.google.com/a/answer/1047213