Increasing surface area decreases pressure (if mass/gravity/... are constant) and keeps frictional forces the same. The interesting question is what the limits of the system are -- when do you transition from static friction (ordinary braking) to kinetic friction (skidding/sliding), which dissipates less energy and doesn't slow you down as well.

The usual metric describing that transition is the "coefficient of friction." It describes the ratio of normal forces (your car pressing down) to frictional forces (your tire slowing down your car) at which you transition from static (good) to kinetic (bad) friction. Tires have a CoF which depends on the pressure (roughly car weight divided by tire surface area, complicated by the fact that wider tires don't necessarily have more surface area on their contact patches). As pressure increases in rubber tires, CoF decreases, so the same normal force (the gravitational force of your car pushing downward) results in less peak frictional force (the ability of your tires to stop you moving forward). Increasing surface area decreases that pressure, increasing CoF, increasing braking ability.

There are multiple parts to the braking system, and all play a part in deceleration.

1) Main slowing effect is braking system converting kinetic energy to heat dissipated by the brakes, and maybe back to chemical energy in the battery in the case of an EV with regenerative braking.

2) As the vehicle slows due to braking effect there's likely to be a mismatch between cars forward speed due to momentum and the rotational speed of the slowing wheels, and the role of tires is to try to maintain a grip on the road and prevent this from turning into a skid. Presumably there's energy being dissipated in the tires (and road) in the form of heat too, but only so much the tires can do if braking is too aggressive.

3) Either the driver, or anti-lock braking system, can pump the brakes to prevent the wheels from locking up since that's not the quickest way to stop.

So, tire contact area with road, and tread pattern, and tire material/construction will all play a role, but overall deceleration of the vehicle is based on a combination of all three of the above factors.