There is no wall jump or wallrun in this game.
To get through the section with walls, you need to use a weapon that shoots spikes that stick into the wall. To get this weapon, you first need to obtain the first part of the chyrograph (in the church using a grenade launcher that you receive after defeating the boss once) and then defeat the boss again with first part of chyrograph. Unfortunately, I didn't have time to explain this section of the game in more detail.
I know what coyote frames are. They would definitely be a good addition, but I didn't think about it when I was quickly making the character controller..