A family of Microsoft products that enable users to capture, organize, and reuse notes electronically.
First, close OneNote completely, then go to iPad Settings > Apps > OneNote > Reset OneNote > Delete Login Credentials
Enable that option, force-close OneNote again, reopen it, and try signing in. Do not enable Delete All Notebooks if you may have notes that have not synchronized. Microsoft documents this credential-reset procedure here:
https://support.microsoft.com/en-us/onenote/reset-microsoft-onenote-between-users-on-a-shared-ipad-or-iphone
Also test both accounts in a Safari private tab at OneNote on the web.
If the problem continues, could you please provide the exact error message or code displayed after the login attempt? This will help determine whether it is related to OneNote or the authentication service.