Omg yisss! as a big fan of parkour in games NEAVE has amazing movement and is very responsive and I absolutely love it! Now for the constructive feedback:
Depending on what your game is going to focused about, You might want to look into "hang time". GameSpot has a great video-interview with a Game Designer/Game Developer from Dead Cells on this.
You handle a lot of different cases which is really impressive. However, you might want to look into allowing players to move more vertical as well:
Example 1:
When jumping against a wall, if you do your ledge-detection and it returns false and the player jumps at the apex, you should allow the player to then jump and switch direction. This new force should (perhaps) be the same velocity as a regular jump but turn 45 degrees.
Example 2:
If the previous exampled has been implemented. That would allow this next example to take place(if the velocity of the new wall jump is strong enough). A design decision would also needed to be made. This is regarding camera direction and the direction of the player. In Mirror's Edge, you press Q to switch the player 180 degrees while in Sword with Sauce direction of the wall jump is dependent on the current velocity of the player.
Lastly, allow me to indulge you to my totally amazing stick figure drawing...
Example 3:
I think this is kinda self-explanatory. ^^
If you have any questions feel free to contact me on twitter @darkphlox
Thanks for the amazing demo and good luck with your game! <3