Outlook 2016 doesn't accept password or app password

The account add problem is a hit and miss situation to start with, so I am not sure if the DNS change truly made the difference, so just by chance aligned with the server started to work again.

I have used most common DNS servers and it doesn't make notable difference. I just changed my phone's device level DNS to Google's and it didn't make a difference to improve EAS-based use cases.

AnotherBug - Yes OAuth is indeed supported for EAS against outlook.com/hotmil.com. As I mentioned before if a developer wants to support that, they would need to do work. It is also totally possible that they did the work to support it for the work accounts, and not did it for consumer outlook.com accounts. That would be a question you need to direct at Google or your client of choice.

I can speak to the outlook.com service that OAuth is indeed supported, and as mentioned gave two clients that were working (Apple and the thunderbird client/add-in).

Two @hotmail.it accounts I couldn't add/configure on Outlook 2016, by setting the Google servers I was able to add/configure. But now when Outlook 2016 starts, there is still the problem of the random password request. So the problem is not 100% solved.

Sorry, I am not sure if I understand what you wrote. Are you saying it works if you set DNS to Google's 8888/8844 or it doesn't work? I have tried use my ISP's DNS, Google's DNS and a few others, and made no difference. And that's assume Outlook use symbolic URL instead of IP address when contacting its servers.

The "Switch to Modern Auth" option in Android's EAS setup screen works... for my work Office 365 account. It does NOT work for personal Hotmail account. I reported this exact issue many posts ago - same symptoms you are describing. I tried let it switch to Chrome browser, Brave browser and even relaxed all privacy settings in the browser and no go, so it doesn't appear to be a browser setting related issue during OAuth authentication. In fact, the same browser and settings works fine when I do my work Office 365 account's OAuth setup. This is also the reason why I challenged MS David's assertion that OAuth is supported on personal Hotmail account. I want to see that be done on a late model Android device but they have never proven it to us.

If this is an "Google issue" then Microsoft needs to work it out with Google. The EAS stack is likely licensed or co-developed, so with MS and G needs to get together to resolve it - if it's truly an issue OAuth support on a particular EAS stack. But I don't believe it to be the case. I actually think some Hotmail accounts, likely the older ones or ones that existed for many many years, are not properly provisioned to support OAuth on EAS.