I generally enjoyed this. I like the character. The level generally works well with your mechanics. The movement itself is flawed.
It looks like your airborn and grounded states are completely identical which looks and feels quite bad. Even raising the aerial max speed by some small amount will probably make jumping feel a lot better.
There isn't any kind of momentum or acceleration in the game. That's appropriate for a lot of platformers but I don't see it ever working for a wallrun centric game like this. You really need to track player velocity persistently to make the wallrun<->airborn transitions feel natural.
I would focus on figuring out the basic physics of the game over adding more moves, animations, making levels, etc.
I wouldn't worry too much about the transition conditions (like what direction do I have to move in to trigger the wallrun vs climbing) Those are generally safe to change without having to replay/touch up every level.