It’s not the orientation of the camera image. Most people do video conferencing with the iPad in landscape orientation and the ipad in a case. With that, the camera is off to the left and lower down. When you look at the middle of the screen, your eyes appear to be staring off to the side. It looks like you aren’t paying attention.Instead of moving it, just make the camera orientation-aware. If it's in landscape mode, flip the image on the camera so it's facing the right way.
Also, when in a case like that, it is natural to have your left hand near the screen for scrolling. When faceID is needed for access or to authorize something, it is blocked by that hand. It happens surprisingly often.