Is there a way to make a wallrunning system using the character controller?

I use character controller for my movement in my game, and I want to make a wall running system. However, all the tutorials I’ve seen all use a rigidbody. Any way I can do this without changing my movement to rigidbody movement?

Depends how you are moving the character controller, but one route you could go down is using collision flags to check if the character is touching the walls, but not the floor:

if (controller.collisionFlags == CollisionFlags.Sides) {
    print("Only touching sides, nothing else!");

You could check for that and allow the player to move as if they are grounded if touching the wall.

You could also try raycasting/capsulecasting to check if there is a wall to either side, and then set up some more specific movement based on where the wall is.