Tire grip is not the limiting factor. Even with skinny 12" tires you can get the rear suspension hopping and break the differential. And hopping (tramping) can happen accidentally so the automaker takes this into account when sizing the diff. Tire grip does have an effect on it, but not usually considered with road cars. With extremes like drag racing slicks it becomes an important factor.

You are all correct, differentials are rated for torque, not horsepower.

The "estimated" ratings given assume a gearbox first gear typical for passenger cars fitted. So for the H145 with a 1.3 liter or less engine, a first gear around 3.7:1. For the H165 cars a first gear around 3.5:1. These gears won't vary too much if it a high-RPM engine, for example if the engine RPM is double, the 1st gear won't be double in practical usage. And Yes, these factors all matter because they are all inter-related, but for practical purposes, a simple torque figure tells the story best.