I've found some threads on Q&A forum about this very issue
https://learn.microsoft.com/en-us/answers/questions/526467/flaw-in-authenticator
https://learn.microsoft.com/en-us/answers/questions/1181201/authenticator-login-loop
https://learn.microsoft.com/en-us/answers/questions/457121/cant-login-to-authenticator https://learn.microsoft.com/en-us/answers/questions/1025256/authenticator-non-ending-loop
None of them have a solid answer on how to rectify the problem except for this one: https://learn.microsoft.com/en-us/answers/questions/1078084/aad-tenant-lock-out-due-to-authenticator-app-reset which suggests calling MS Support.
I called MS Support for my country (NZ) and got the following phone menus
1 Home users 2 Business users1 Microsoft 365 products such as Sharepoint Online1 Use business email address containing company domain1 Technical support2 Billing subcriptions or activations3 Purchase microsoft solutions for business use4 Cancel subscription2 Personal email address - hotmail, outlook, MSN3 Microsoft partner network2 All other enquiries1 Product activation2 Technical support3 Licensing assistant4 To purchase microsoft solutions for business use5 Visual studio, mirosoft certifications, academic programs3 Microsoft Partner Network members
2, 1, 1, 2 - Got through to someone who told me to hang up and choose 'Azure' from the phone menu (which as you can see, doesn't exist)
2, 2, 2 - Got an automated message telling me to contact Microsoft online. Uhhm, no, that doesn't work. 2, 1, 1, 1 - Got through to someone who told me to get my administrator to deactivate the authenticator app via the Azure Administrator Portal (or something like that), and if the admin themselves had trouble, to call MS support Global Customer Service numbers.
I will try to get my manager (who is our Microsoft admin) to call customer service and see if he can get my Authenticator deactivated.
AniOR - I suggest calling MS Support and choosing 'Home user' option, see if they can help.