Visualising downwash over a finite wing
Downwash is a misleading concept when discussing airfoil lift. Instead, just focus on the pressure distribution around the airfoil.

If I understand your confusion correctly, you are picturing, correctly, that there is an overall low pressure on top and an overall high pressure on the bottom, then why isn't air flowing from high pressure to low pressure?

This will indeed be the case, if there is no airflow. What you are missing is that, the static pressure distribution is caused directly by the airflow around the airfoil. The distribution is steady-state, because the combination of dynamic pressure and static pressure resists further changes; it's at an equilibrium.