I am also having this problem in the full release of Monterey. 11.01 In addition to the full screen not working I have noted the following:
When I use Applescript to "Fit To Screen" in a shortcut, it will work for the FaceTime window ONLY when the program is activated but NOT connected on a call. When it is actually connected on a call, the shortcut will not change the screen.
When I am calling into a Monterey OS M1 Mac Mini with FaceTime and iOS 15.1.1 , strange things happen to the screen size on the Mac mini based on the orientation of the iPhone 12. If I start with FaceTime at the maximum size and I answer the iPhone in landscape, the size remains. As soon as I turn the phone to view in Portrait, the FaceTime window on the Mac remains at the max height, but slims to about 1/3 of the screen. (Seems normal, but there is more.) When I switch back the iPhone to Landscape, the window on the Mac Mini keeps the "portrait width" of about 1/3 of the screen and squashes the window down to match the spec ration of the iPhone. Now the window is about 1/8 of the total Mac Mini screen. When I switch back to hold the phone in portrait orientation it keeps the width and only grows back to a very small portrait window. Nothing ever gets back to even close to max height or width.
In addition, the Full Screen menu item on the Mac Mini is always dimmed and unavailable any time, whether a call is active or not.