Outlook 2016 doesn't accept password or app password

All you need to know:

Modern Authentication Methods now needed to continue syncing Outlook Email in non-Microsoft email apps https://support.microsoft.com/en-gb/office/modern-authentication-methods-now-needed-to-continue-syncing-outlook-email-in-non-microsoft-email-apps-c5d65390-9676-4763-b41f-d7986499a90d

Basic Authentication interim experience

Until September 16th, users signing into Outlook.com through Basic Authentication may experience recurring password prompts in Outlook and other third-party email applications. This is a known issue. After September 16th, users attempting to connect their Microsoft accounts through Basic Authentication will fail to do so.

The following versions of Outlook Desktop do not support Modern Authentication for Outlook.com:

Outlook 2007, Outlook 2010, Outlook 2013, Outlook 2016 MSI, Outlook 2019 LTSC. Any release of Outlook Desktop with a version less than 11601.10000 does not support Modern Authentication for Outlook.com.

Just received in one of my Hotmail accounts an ‘Action Needed – You may lose access to some of your third-party mail and calendar apps’ email which includes the link to https://support.microsoft.com/en-us/office/modern-authentication-methods-now-needed-to-continue-syncing-outlook-email-in-non-microsoft-email-apps-c5d65390-9676-4763-b41f-d7986499a90d admitting to the intermittent login issues. This should have been sent months ago. I wasted far too much time trying to figure out what has been causing the intermittent login failures until I discovered this thread. Very annoyed with Microsoft.

So my version of Outlook that I installed will no longer support Basic Authentication? How do I know if it is an Outlook 2016 MSI version?

HI.

So my version of Outlook that I installed will no longer support Basic Authentication? How do I know if it is an Outlook 2016 MSI version?

From: Modern Authentication Methods now needed to continue syncing Outlook Email in non-Microsoft email apps

https://support.microsoft.com/en-us/office/modern-authentication-methods-now-needed-to-continue-syncing-outlook-email-in-non-microsoft-email-apps-c5d65390-9676-4763-b41f-d7986499a90d

If you use Outlook for Windows: 

Outlook supports Modern Authentication in all current Microsoft 365 subscription SKUs and Outlook 2021 LTSC (any SKU with build 11601.10000 or higher) when connecting directly as Outlook.com. If your Outlook is configured to connect to Outlook.com using POP or IMAP, Modern Authentication is not supported. This means that when Basic Authentication is fully deprecated, it will no longer connect.  For this scenario, you have a few options:

Option 1: Get a newer Outlook email app which supports Modern Authentication

If your Outlook client does not support Modern Authentication, you will need to upgrade to the latest version and then setup using Outlook.com Sync. You can either purchase a new Outlook License, use the Outlook that is included in your Microsoft 365 subscription, or download Outlook for Windows for free.  

Option 2: Switch to Outlook.com/Exchange Syncing

Instead of using POP/IMAP and SMTP, create a new Outlook Desktop profile and then add your Outlook.com account using automatic account configuration, which will add the account with Modern Authentication. To do this, please use the following guidance:

1. Create a new Outlook Desktop profile. For more information, please go to Create an Outlook profile.
2. Add your Outlook.com account. For more information, please go to Add an email account to Outlook.

The following versions of Outlook Desktop do not support Modern Authentication for Outlook.com:  Outlook 2007, Outlook 2010, Outlook 2013, Outlook 2016 MSI, Outlook 2019 LTSC. Any release of Outlook Desktop with a version less than 11601.10000 does not support Modern Authentication for Outlook.com.

Outlook apps are available for free and can be downloaded directly from the Microsoft Store on Windows, the Mac App Store, iOS App Store, or the Google Play Store.  

After your download the new email app, add your accounts and they will all be configured to use Modern Authentication and sync properly, helping keep them safe.

It doesn't matter if it's MSI or not. Only 2021 and later will support OAuth for the free MS email accounts.