I have no idea on the case of high end sports cars.
But for most passanger cars I’ve driven I felt within the oem specs the narrower tires with smaller rims gave me more responsive braking and shorter stopping I felt.
The short answer is yes, wider tires absolutely decrease stopping distance when all other factors are the same.
The two factors that matter most for braking are grip and weight. Larger tires provide a larger surface area for tire contact. More surface area = more grip.
Larger surface area provides more grip which decreases stopping distance.
Not true. The size of the contact patch is exactly the same in number of square inches. It’s wider, but shorter front to back.
Why is the contact patch shorter front to back…?
Because the load is now spread across the width