flightoffancy writes:

But airfoils aren't planar, they are curved. Why do varying curvatures
of airfoils significantly affect wing lift / stall speed?

They don't affect lift, they just affect drag and stall speed. I don't know
the theory well enough to comment on why this is so. From a piloting
perspective, it is only necessary to know that AOA determines lift, and the
shape of the airfoil is irrelevant.