I  have a 2017 iMac Pro running Monterey 12.5 . When I launch Studio within Canvas, I can access my computer's camera in Webcam Capture, but when I choose Screen Capture and want to record "Both" I click on the "Select Webcam" option and no camera list appears. The link just turns blue. Since I am unable to select a camera - it never asks for permission to use the camera - ergo, Screen Recorder does not appear in the apps list which can use the camera in Privacy Settings. If I boot in safe mode - I CAN choose a camera from a list, but my computer cam is not on that list. I have uninstalled, reinstalled, tried different browsers, trashed every app that I don't need along with their preferences. My IT folks are working with me, but so far no solution. 

I tried the process using another iMac Pro in the department and it works fine.