>> "Log into the web based version and sign out of your account from the right upper corner"
This will only sign you out of the Web Based Outlook. i.e. Next time you open "outlook.com" in your browser it will take you to the Microsoft Account Login page.
BUT - This has no effect at all on the New Outlook For Windows app on a PC. It will go straight to your Inbox.
The only method I have found that works is to Sign out of your Microsoft account everywhere. Follow the instructions on this Microsoft Support doc.
It took about 8 hours but I was finally and completely signed out. Next time I open Outlook it would pop up the Microsoft Account Login dialog. Closing the account login dialog a few times, without entering any credentials, would not get me in. Only a Sign in failed.