I managed to make this disappear for a few days by *completely* removing the account: remove it from account settings (from all devices), let the removal sync to other devices, reboot, and remove it from the sql accounts database:
/usr/bin/sqlite3 ~/Library/Accounts/Accounts4.sqlite 'DELETE FROM ZACCOUNT WHERE ZUSERNAME = "my@email"'
Then add the account again.
This worked for a few days. Now the popup is back again.
I don't actually need to enter the password—the account works without it—but the system keeps nagging and nagging and nagging and nagging about it. Every wakeup from sleep, and sometimes just randomly while using the computer. The university providing the account enforces M$ proprietary MFA and doesn't allow application-specific passwords that are according to the useless IT department supposedly "incompatible".
This is in latest macOS 12.2.1, so the "Apple recommended" comment above doesn't help at all.