Definitely not apples to apples for those two tires.

Regarding those tires "just giving the car more overall grip," more grip will put higher loads on its springs and dampers, for instance, which may lead to undesired handling traits (underdamped suspension, probably). The car can and will pitch and dive more dramatically with more grip. We're talking jumping from 1g to 1.18g increase in lateral acceleration - that's 18%, which isn't insignificant! In transient moves, you might see a 25% increase in grip plus you're moving more quickly while doing so. That can upset the traction and handling systems as well, if they aren't calibrated to deal with the additional speed of the car getting loose or out of shape.

I have no direct experience with a 991.2 and adding stickier tires. Maybe it is just that simple, as you say, and there are no issues with adding stickier tires. 10 or 20 years ago, I'd have definitely agreed with you - cars were much more basic and far less complicated. Nowadays, it seems like cars are much more sensitive to changes because everything (ABS, traction control, stability control, launch control, variable steering rates, etc) is tied together to the engine and all drivetrain sensors around the car.

I was going to post about having similar caliber tires to equalize the handling a bit as well

If I were made of money I would open a YouTube channel, hire a good track driver, and just test cars on same tires all day for shits and giggles. I understand cars are engineered for the tires they come with but I still believe the 911's handling isn't far off from the GS if it had better tires