Nice concept, I liked the artstyle and sound. Brings up memories of some old platformer games from childhood :) The lighting system makes the dungeon climatic, you could even consider to make it darker overall.
Wallclimbing is buggy. When you drop from edge without jumping and then come near wall the wallclimb animation does not play and character can't climb upwards. Sometimes I feel like part of game is thinking that player is wallclimbing and part is not. I took fall damage because of that in a situation when I certainly should have not taken it (I dropped from wall just above the floor and still took fall damage). Also for example when climbing down the wall and holding move towards wall player gets stuck on wall corner. Just pointing out things here to help you fix it but I guess you probably are aware of these issues.
The autojump on edge should be disabled by default imo. Knowing when to jump is a huge part of platforming and this is taking it away, and sometimes it even is annoying if you want to drop instead of jumping. But this is just my opinion, you do what you want :)