If the saddle is the only thing you've changed on this bike, look at that. I usually have problems when my saddle is not in the right fore/aft position. Remember - moving your saddle up and down also moves it forward and back since your seat tube is at an angle. Get your height set then try moving the saddle forward and back on the rails until you find the sweet spot. This fore/aft placement of the saddle determines where your knee is relative to the pedal spindle.

Centering cleats over the ball of the foot is pretty standard. It's not the fore/aft positioning of the cleat that is usually the problem. In my experience it's more often having the cleats angled wrong. Have you tried riding without the clipless pedals since the pain started?

If the pain worsens with climbing, maybe you are trying to push too big a gear. You would not be the first. Climbing seated with too big a gear on a saddle that is too low = ouch for most people.