Determine Direction of Movement based on Camera and Player Direction

I have a 3rd person camera that follows my player at an offset. For example (-10, 15 -10).

The player’s movement can then be calculated based on the camera’s offset.

Camera cam = Camera.main;
Vector3 forward = cam.transform.forward;
Vector3 right = cam.transform.right;
forward.y = 0f;
right.y = 0f;
forward.Normalize();
right.Normalize();

Vector3 direction = forward * Input.GetAxis("Vertical"); + right * Input.GetAxis("Horizontal");
            
Vector3 velocity = direction * speed * Time.deltaTime;

controller.Move( velocity );

LookAtMousePosition();

The player will also look towards where the mouse position via a ray cast.

    private void LookAtMousePosition() {
        Ray ray = Camera.ScreenPointToRay(Input.mousePosition);
 
        if (Physics.Raycast(ray, out RaycastHit hitInfo, maxDistance: 300f))
        {
            var target = hitInfo.point;
            target.y = base.transform.position.y;
            transform.LookAt(target);
        }
    }

Now I need to set an X and Z variable to determine animation to play in a 2d blend tree.

anim.SetFloat("walkX", someRandomX); 
anim.SetFloat("walkZ", someRandomZ);

I think that I need to subtract the normalized direction the player is moving from the normalized direction the player is looking. But with all these different coordinate systems I am not able to figure out how to get the correct animation to play in the blend tree.

Anyone able to tell me how I should be thinking about the math here?

I have resolved this by switching from using vectors to angles.

float angle = Mathf.Atan2(direction.x, direction.z) * Mathf.Rad2Deg;
float animAngle = (transform.eulerAngles.y - angle) + 90;

I was bashing my head against something similar. Thank you