After re-installing Catalina, I added greenshot app via AppStore again. The App appears in taskbar. When using Greenshot, the dialogue "Greenshot needs permission to capture your screen" appears.
When navigating to System Preferences -> Security -> Privacy -> Screen Recording, the area on the right (where the app should appear) is empty. I cannot drag& drop the app to this area either.
-> Greenshot not usable at the moment. > blocker
MacOS Catalina 10.15.5, iMac late 2013 i5