Dear Mika Arian
Greetings!
Thank you for posting on Microsoft Community!
Based on your description, I understand your issue regarding "Cannot access account with Authenticator because it wants me to use Authenticator to authenticate" and we apologize for the inconvenience caused to your work!
Would you please kindly try signing into My Sign-Ins (microsoft.com)? Please select I can't use my Microsoft Authenticator app right now and try signing in via other methods you've added. Then you can manage your sign-in methods there. You may try to delete Authenticator as a method and set it up again.

If the above method failed to you, then you may have to reset MFA options for this account.
If other user has admin rights, it is suggested to contact your admin and ask admin to reset the Authentication method for your account. Admin can do it by follow Manage user authentication options. (If you are not sure who is your admin, can refer this How do I find my Microsoft 365 admin? - Microsoft Support).

If you are the admin only and can’t access your account due to Authentication issue, it is suggested to contact Data Protection team, because we are from community team and we are not authorized to reset any user/admin account. Data Protection Team is the only support team to check and reset account. To find contact number of Data Protection team, please check Find Microsoft 365 for business support phone numbers by country or region - Microsoft 365 admin | Microsoft Learn or Global Customer Service phone numbers - Microsoft Support.
Thank you so much for your precious time and co-operation. I wish you all the best!