Dear Nino Kereselidze1,
Good day! Thank you for posting to Microsoft Community.
I am sorry not able to sign in to your account due to authentication app. May I please double confirm if you are setting up Multi-Factor Authentication (MFA) for the first time? If yes, this seems to be a recent known issue and the team is working on an immediate fix. therefore, you may try to check on different browser or wait just 1-2 days and try again to check if the fix is implemented. I will also update as soon as the service restored on my side.
However, if you have previously set the authentication method before, I do understand your query here, but as you are using school account, I sincerely recommend you contact your college IT admin to reset multifactor authentication session from their end in the Microsoft 365 admin account, to be able to add your account to your authenticator app and sign in to your account. It's important to note that since we have limited resource and privileges as Microsoft Customer Support, we are not allowed to examine institutional end users account authentication scenario. If the accounts are educational or organization-managed, only the owner or IT staff of that school or organization has the right to manage accounts, including resetting the account multi-factor authentication, allowing account to change authentication methods and changing phone number for authentication method. Therefore, I sincerely recommend you reaching out to your school IT admin or the person who is in charge of managing Microsoft 365 admin center of the school. The admin can refer to this article, to be able to reset the multifactor authentication session of your account in the Microsoft Entra ID admin center, see Manage authentication methods for Microsoft Entra multifactor authentication - Microsoft Entra ID | Microsoft Learn
Thank you for your precious time and kind understanding.Have a nice day.Sincerely,Libeamlak | Microsoft Community Moderator