How to grant Screen Recording permission to an Automator Quick Action
I have had some similar issues. My workaround was to add the Automator created app to:
System Preferences → Security &amp; Privacy → Accessibility
Then running the app, letting the system add the programs it may control to:
System Preferences → Security &amp; Privacy → Automation
This might not at all be what you asked for, but I thought it seemed a bit similar.
Note however, every time I change something in the app, I have to repeat the above steps.