Wall climbing: I have now realized that it happens too quickly, and will make sure to take that into consideration in the future.
Jumping: I don't see what's so inconsistent about jumping. Is it the responsiveness, height of jump, or something else?
Screen response: I have been aware of this issue for a while, but I never truly found a solution, because there are many different situations where any code that controls how the camera should follow the player becomes jarring. I had even tried Cinemachine, but that sometimes went off screen, and got buggy when I tried returning it to the player. DL;TR: I was aware of the jarring response of the camera, but couldn't find a fix.