Mojave App Store shows "UPDATE" instead of "GET"

One of my apps glitched and stopped logging me in. It's not 32-bit, afaik, and has performed well all the time before. After reboots and relaunches I have decided to reinstall the app, so I put it to the Trash. I've searched for library and other files mentioning the app, and has them all removed as well (at least the ones I've found with simple app name search).

The only option the app develop provides for MacOs installation is App Store download, so no dmg to reinstall.

But the button shown in App Store is 'UPDATE' not 'GET' and it does nothing, and no system restart no logging out-in seem to have any effect.