Using Classic Outlook on Windows for personal email, calendar, and contact management
UPDATE:
Well overnight, the rocket scientists at Microsoft released a new version of Outlook with the SAME VERSION NUMBER (2401), but a new build number (16.0.17231.20194). This did NOT remove the annoying App Search bar! The App Search bar is still totally useless as well (i.e. it doesn't work) and there is still no option in File-->Options-->Advanced to turn it off.
Version History Link from Microsoft to see this for yourself: https://learn.microsoft.com/en-us/officeupdates/current-channel
Beyond the obvious fact that they didn't fix this issue, I find it disturbing that Microsoft labeled this new release with the same version number (2401). It appears they have done this in the past though with version 2312. At least they changed the build number.
If you still want to install the new release, you can do manually by navigating to File-->Office Account-->Update Options-->Update Now.