discouraging climbing

Spray away....  I have pet screen so when moths or other insects get to teasing, kitty will want to play.

I use water and it helps but sometimes distracting them with a laser has helped me, good luck with Doom

You could try spraying the screen with a scent that puts him off. Most cats hate citrus scents. Maybe get some lemon essential oil (like you'd use for aromatherapy) and put some in a spray bottle with water - 1 drop oil per 10ml water. Spray the screens with it, and be sure to shake well before each use.

You could put some latticework up inside the screen, i.e., cut a cheap plastic or wire trellis to size. When our last cat was a small kitten and climbing the screen in our kitchen window, I temporarily taped an oven rack over the screen.