Today, I updated Catalina to 10.15.2 and was using 10.15 or 10.15.1 before that. Skitch 2.8.4 from App Store used to work fine with the "old" Catalina versions; with 10.15.2, nothing at all happens when I push the screenshot (fullscreen or area or timed area) button in the Skitch app.
Skitch has the screen record permission in Settings-Security-Privacy-Screen Capture.
Is that a known defect?