Catalina - App Store issues - doesn't automatically find new updates and cannot update!
I ran into this problem in Big Sur (currently Public Beta).
I also noticed that App Store apps that I had on my system were showing up in my App Store account list as though they were available to download but not installed.
I tried various methods including deleting App Store caches and preferences files, deleting the keychain item (search in Keychain.app for appstored), and signing out and signing in to the App Store.
In my case, the problem was that Spotlight was no longer indexing /Applications for some reason, even though /Applications was not excluded from indexing.
I opened Terminal and ran:
sudo mdutil -a -i off

then
sudo mdutil -a -i on

And shortly afterward, the App Store showed available updates, and my installed apps were showing up as installed in the App Store as well.