The wing has a pressure gradient along the AB direction, is there a pressure gradient along the CD direction?
Yes, but a weaker one than in lengthwise direction.
You can observe the local pressure by comparing the distance between two stream lines. When they move closer together, speed goes up and static pressure goes down. As you move away from the airfoil, the distance between stream lines recovers to its value at infinity.

Stream lines around airfoil (picture source).
This effect depends on the Mach number of the flow. At very low speed, the recovery is rather quick because speeding up contracts the airflow so it is easy to make way for the airfoil. At higher (but still subsonic) speed, speeding up is coupled with a drop in density, so the contraction is less pronounced and it takes more height for the disturbance to die down. At supersonic speed, the pressure change is sudden (in a shock or an expansion fan), and the pressure rise of a shock reaches into infinity.