Apple aren’t actually designing its own sensors, are they? I expected they would be using an off the shelf Sony sensor just like (most) everyone else.

I generally disagree with your premise here. Yes, you can do some pretty amazing things with image processing in software, but you have to have a decent starting point. A good example of this is just how minimal the image processing improvements are in the M1 MacBooks compared to their Intel counterparts — marginally better, but nothing to write home about.

I’m not at all an expert in optics, but I would expect the biggest constraint is the available depth for the lens and camera sensor within the upper clamshell of a laptop vs a phone. It doesn’t seem like it would be a huge difference but an extra millimeter or so makes a huge difference in the size of the sensor that can be used.