Could you edit your post to make it more clear which gif corresponds to which code? Do I understand correctly that "Keyboard Is key code down+Trigger once" works fine, but "Keyboard On key code pressed" glitches?
I would start by checking if these two events are triggered in the same tick. Enable both events and add Browser Log "On key pressed" & tickCount and Browser Log "Is key down" & tickCount. Run the game and check browser console.
Also, because On Key pressed is a trigger, it may be executed at the beginning of the tick, before some other events in your game essential for wall climbing.