Using Classic Outlook on Windows for personal email, calendar, and contact management
Sounds like you've gone above & beyond in testing to troubleshoot this problem. - Thanks for the detailed writeup and sharing your experience so far.
I've been seeing the constant password prompt across multiple 'outlook.com' accounts in use with both Outlook 2016 & 2019 desktop clients.
Clearing entries referencing the email account in Windows Credentials Manager & creating a new Outlook profile appeared to temporarily alleviate the issue on some of these accounts. However the issue would then reocurr several days later.
Ultimately resetting/changing the password seems to have been more successful, but I'm still intermittently seeing the authentication prompt despite entering the correct password (works without issue via OWA in the browser). Weirdly when this happens the inbox will sometimes still sync in the background even though the "Needs a password" status can be seen on the exchange connection info at the bottom of the window.
I've also enabled "Troubleshooting Logging" under the Advanced Outlook settings which has helped diagnose past issues. Unfortunately with this particular problem the logs don't list any evident errors; I'm ultimately convinced this is a problem on Microsoft's end. Especially with numerous email accounts experiencing the same issue in a roughly similar time period!
I considered the route of enabling 2-step verification using App passwords instead, but it sounds like you were still seeing the same issue despite having this enabled.