I suspect the forces in the spring side and damper side are fairly close. The spring proceed a force relative to the displacement of the suspension – so how much travel you’re using, and the damper provides a force dependant on the speed of the suspension is working, so it’s not as if it is all one sided. If the damper was providing a force significantly less than the spring then you’d feel very under damped, and vice versa if the damper was providing too much force.
There is a whole load of twisting going on with the wheel, frame, large volume tyres etc. so you’re not going to notice the flex of the fork chassis too much.