Good day and I’m sorry to hear about the difficulties you’re experiencing.
Based on the information you've provided, it appears that your account is currently configured to use the Microsoft Authenticator app as the required verification method. Since you were signed out of the app and no alternative authentication methods (such as email or SMS) are available, you're unable to complete the verification request and access your account. This can occur if the Authenticator app was removed, reset, or lost access to the account, leaving you unable to approve the sign-in prompt required to regain access.
In this situation, the most appropriate next step in most cases is to contact your university’s IT administrator.
Please ask your administrator to follow the steps outlined in the guide below to revoke existing MFA sessions and require re registration.
Manage authentication methods for Microsoft Entra multifactor authentication - Microsoft Entra ID |… This process usually only takes a couple of minutes.

Once this process is completed, all existing sign in sessions will be cleared. The next time you sign in, you will be prompted to set up Microsoft Authenticator again from the beginning, and verification codes should be delivered normally. If appropriate, you may also wish to ask your administrator to add an additional authentication method, such as SMS or email, to help ensure continued access in the future.
If you’re unsure who your Microsoft 365 administrator is, the following article can help you identify the correct contact at your school: How do I find my Microsoft 365 admin? - Microsoft Support
Please note that this is a user to user support forum, and I do not have access to administrative tools or permissions to reset or modify MFA settings on your account. Because your account is managed by your school, only an authorized Microsoft 365 administrator at your institution can make these changes.
I hope this information helps point you in the right direction and allows you to regain access to your account as quickly as possible. If you have any further questions or need clarification, please don’t hesitate to reach out. I’d be happy to assist.
Thank you for your patience and understanding.
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