HI,
I had this same problem and tried a few things. Yes, in System Preferences you have to click access for the camera and the mic, but in my MacBookPro I just found you also have the red square for "Screen Recording" a few more icons down in the same menu. You have to click access for Screen Recorder Launcher in this too. I just did a test and I can now record my slides as well as the little video box that I can place in the corner of the slide (spent hours trying to get this going!).
I'm not a tecky, but perhaps this is an added security measure for MacBookPros (?).
Thanks for the info from others, thought I'd share this because it is a huge relief.
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