Why is the air pressure lower on rainy days than on sunny days in the same area?

Because the cold air and rain make the temperature in this area lower, you know that in a relative space, the lower the temperature, the lower the air pressure, which is why the air pressure is lower in rainy weather.

Also, you know why there is a strong wind during a thunderstorm, because the air pressure difference caused by rainfall will replenish the air in other areas, and the wind will basically stop when the rain stops.

You must have such an experience.