Outlook 2016 doesn't accept password or app password

I am not aware of any Outlook.com report that will show Classic Outlook sign ins. This is good feedback, and I will share it back to the Outlook.com Team. The M365 Admin Center will show client activity including Classic Outlook in some of its reports e.g. https://admin.microsoft.com/Adminportal/Home#/reportsUsage/EmailClients. 

Since you are getting the Windows Security prompt there must be some residual in the Outlook profile for the basic auth credentials. This might be difficult to isolate and fix. I know creating a new Outlook profile is a hassle but if you get a chance, please try that and see if it still has the prompt.

No. It's the normal Outlook dialog that looks similar to the ones on the older Outlook version that prompts for authentication. The one you showed is the OAuth/OAuth2 prompt, which I recall I got when I added the account to Outlook. It's not the prompt I am getting now. Plus, the logging session shouldn't time out, so I really shouldn't see this dialog.

Outlook is activated and logged into my work account, which is also the main account listed under "Account Settings".

Connection Status Dialog shows both accounts as having "Bearer*" under Authentication.

Profile was already rebuild recently due to another Outlook issue and that was from the support runaround I got. The "Report Phishing" button disappeared for over 2 months. Support was clueless until it was escalated after 2 months of back and forth. Turns out, the removal was due to Report Phishing being EOL'ed and moved to a new method of doing Report Phishing but no article was published about that.

By the way, where do I got to see active logged in session into Hotmail/Outlook accounts? I can go to Outlook Web->Setting button->search "Mobile" and find my phone listed as one of the connected session/device but I don't see my Outlook desktop as listed. If I goto my MS account settings and security, login history, all the history I see are related to Outlook Web session and does not include Outlook for Android or Outlook for Windows.

Is the auth prompt the Windows Security prompt or like this one below?

If you click File, Office Account, under User Information, make sure you are signed in there with the account you got the subscription and no errors there.

Check the Connection Status Dialog if the Status shows any connections not Established when the auth prompt shows up. To see the Connection Status Dialog, locate the Outlook icon in the System Tray, press the Ctrl key, right click Outlook icon and click Connection Status.

In case there is some issue with the Outlook Profile, use the steps here to create a new one, Create an Outlook profile - Microsoft Support. You can keep the old profile or delete it later once you know everything is showing correctly in the new profile.

If the issue persists check if you have the option Help, Contact Support in Outlook Subscription and open a ticket from there.

It's showing as Microsoft Exchange already. On that screen you showed, I have two accounts, one is my work and the other one is the test Hotmail. My work email doesn't give me prompt for authentication but the Hotmail one does. Outlook version is 2407.

EnableADAL key doesn't exit in my registry. I don't know the default state of this. I have added it and set to 1, no difference.

I have a coworker doing the same for his outlook.com personal account and see the same issue. The authentication prompt is not as frequent as before but it definitely pops. In fact, that dialog has a "stay on top" behavior, so I have seen his pop during screen-shared Teams meeting.

POP3/IMAP is not longer used in Outlook desktop for hotmail/live/msn/outlook.com mail is a good thing. Exchange or EAS should be used to sync contacts and calendar as well. Those are syncing, so that's another indication I am on Exchange with this hotmail account.

In Outlook click File, Account Settings, Account Settings. Make sure the account shows as Type = Microsoft Exchange. If it is not, you can try removing it and add it back as Exchange or create a new Outlook Profile, Create an Outlook profile - Microsoft Support. Now that Basic Auth is being deprecated Outlook does not support adding Outlook.com accounts as POP/IMAP.