iPad FaceTime camera misalignment

As described, your iPad is not defective. What you are seeing is a fundamental limitation of tablet and camera design - which becomes more pronounced as screens become larger…

By necessity, the iPad camera is off-axis; the bigger the screen and the closer you are to it, the more this physical limitation becomes apparent. This effect is not limited to iPad, but similarly affects all computing platforms that employ a front-facing camera.

Unless you are looking directly at the camera, your gaze will never appear to be looking in its direction. Ultra wide-angle lenses, such as that employed by your sixth generation iPad Pro, seem to visually exaggerate this effect - hence the behaviour that you observe.

When comparing with a desktop or laptop PC, the camera is often placed at the top as opposed to the side of the screen. As such, when using a computer (or an iPad Pro M4 and iPad Air M2) with the camera located at the top edge of the screen, your gaze may appear to be below and away from the camera axis - whereas your sixth generation iPad Pro will appear to have your gaze to one side. A correctly positioned laptop will have the top-edge of the screen (and hence the camera) approximately at eye-level. Whilst your gaze will still be directed downwards, the off-axis effect will be minimised.

In conclusion, there is nothing that you can do - other than to (a) place the screen slightly further away to reduce the unavoidable effect - or (b) use your iPad in Portrait screen orientation.