Claude app monitors input and screen without permissions on Sequoia

Hi. I have just hit something that looks like a giant security blackhole to me. I installed Anthropic's Claude app on Sequoia 15.7.5. I noticed Claude app can monitor keyboard input even when the focus is on any other application. For example, when Claude app is open hitting Alt key twice will show Claude popup overlay prompt regardless of the app you are currently in.

Normally apps need explicit permission for background input monitoring, they need to be in the allowed app list under System Settings -> Privacy & Security -> Input Monitoring and enabled. However here's the thing - Claude app can still somehow monitor input without being on the allowed list. In fact I have no apps at all on the Input Monitor list.

Further more, it appears to have access to screen recording as the popup prompt can track windows behind mouse cursor and is showing a "Send a screenshot of ..." banners above whatever app window is under cursor. Again, without being listed and enabled under System Settings -> Privacy & Security -> Screen & System Audio Recording.

The only place Claude app is listed is under System Settings -> Accessibility (Allow the applications below to control your computer) and it is disabled!

In the Claude's app own settings "Let Claude tale screenshots and control your keyboard and moue in apps you allow" option is also turned off.

Any ideas what is going on and how to block Claude app access to input monitoring and screen recodring?

Thanks

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[Edited by Moderator]