Thank you for posting in Microsoft Q&A Forum.
Based on your description, could you kindly confirm whether the school account you mentioned is provided by your institution? Typically, these accounts have a format such as @schooldomain or @edu.
If that is the case, the situation you are experiencing is likely due to the MFA policy in your tenant requiring Authenticator number matching for all sign-in sessions. Since you have not yet added the account to the app, you are unable to complete verification. Therefore, you will need to reach out to your school’s administrator (the person who provided your account and has full permissions to manage accounts within your institution).
If you're unsure who the admin is, please see: How do I find my Microsoft 365 admin? - Microsoft Support
Please kindly ask them to refer to this article to help reset your MFA settings: Manage user authentication methods for Microsoft Entra multifactor authentication.
Once the reset is complete, please follow this article to add your account back to the Microsoft Authenticator app: How to add your accounts to Microsoft Authenticator.
I hope this helps. Please don't hesitate to let me know if you have any further questions or concern.
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