repechage

they flex under load, do not equate with modern pedal designs, they also flex but not as much.
So, what happens is that under load, the pedal bends the foot as viewed from the front, which also changes the alignment of the two lower leg bones and in turn loads the knee differently. As the load on the pedal is not constant through the crank cycle, there is unwanted movement.
A similar situation can happen with a bent pedal spindle. Way back we had a few customers who came into the shop complaining of knee pain, we looked at their pedals for major gouges on the end for major dust cap damage. Sure enough, bent pedal spindles. One guy did not believe it, so we traded that pedal for another. He came back a week later, no more knee pain. He bought a new spindle then and we installed it. It is a challenge to observe the problem, but it happens.
In the steel crank days I was told the cranks could be suspected too.

poor cleat placement can also screw up knees pretty fast. I have come up to many a rider where they pedal in such an observable uncomfortable way. The knee swinging in and out through the crank rotation. I have when possible asked such riders how their knee pain was. They all wonder how I knew! Go have your cleats readjusted or professionally set, that will surely help!