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Since this email address was issued by your college (ending in .edu), this is considered a Microsoft 365 Education account.
And when you change to other phone, the Microsoft Authenticator app doesn’t automatically transfer your account settings because the multi-factor authentication (MFA) configuration is linked to the specific device where it was originally set up.
For security and privacy reasons, Microsoft Support does not have access to manage or reset passwords for school-managed accounts. Microsoft provides the software, but your school acts as the administrator.
You must contact your School’s IT Help Desk or Student Support department. They are the only ones with the administrative access to reset your password or verify your identity to unlock the account. Let them know you are locked out and that the self-service recovery is failing. They will manually reset it for you based on this information: Manage authentication methods for Microsoft Entra multifactor authentication - Microsoft Entra ID | Microsoft Learn
For additional information, you can refer to: Common problems with two-step verification for a work or school account - Microsoft Support
I hope this information helps.
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