Using the New Outlook for Mac features in educational settings
Hi @Julia Markl
I understand that you are experiencing an issue with the MFA method for your university account. Since you are unable to sign in to your account through the Microsoft Authenticator app, the authentication approval request cannot be completed, which is preventing you from accessing Outlook.
To resolve this issue, because this is a school account managed by your university's IT department, you will need to contact your university's IT administrator if you no longer have access to your registered MFA method. They can reset your MFA settings or require you to re-register your authentication methods.
Once the MFA reset has been completed, you should be able to sign in to your account again and set up Microsoft Authenticator during the sign-in process.
You can ask your IT administrator to follow the guidance in the following Microsoft Learn article to manage and remove your existing authentication methods: Manage authentication methods for Microsoft Entra multifactor authentication - Microsoft Entra ID | Microsoft Learn
I hope this information helps and if you have any question, please feel free to ask via comment section.