How to move character controller only on X and Z axis but not on Y.

Hello, I am very new to programming in Unity and programming in general, so please forgive me if I don't describe my question very well or if I ask extremely nooby questions.

I've set up an FPS player controller that moves using WASD, and can also look around using a mouse look script. I used a transformdirection so that, for example, if I look to the left and press W, I will move forward in that direction. The problem is that it does this on all three axis x y and z. I only want this to occur when looking left, right, or forwad. (X and Z I think, but correct me if I'm wrong.) What I don't want is to move upwards if I'm looking up or downwards if I'm looking down (Y axis)

So using the script I have, how can I make it so I move forwards where I'm looking that isn't up or down relative to the world?

Also since I'm very new to coding, if I have any problems with my script or if it's using some bad practices that I'm unaware of please let me know.

Here's my code:

 // Use this for initialization
 void Start () 
 {
     
     controller = GetComponent<CharacterController>();

 }
 
 // Update is called once per frame
 void Update ()
 {
     //WASD movement
     if(controller.isGrounded)
     {
         
         
         movement = new Vector3(Input.GetAxis("Horizontal"), 0f, Input.GetAxis("Vertical"));
         movement = transform.TransformDirection(movement);
         movement *= speed;

         
     }
    

     controller.Move(movement * Time.deltaTime);
     movement.y -= gravity * Time.deltaTime;

     //Mouse Look 
     if (axes == RotationAxes.MouseXAndY)
     {
         float rotationX = transform.localEulerAngles.y + Input.GetAxis("Mouse X") * sensitivityX * Time.deltaTime;

         rotationY += Input.GetAxis("Mouse Y") * sensitivityY * Time.deltaTime;
         rotationY = Mathf.Clamp(rotationY, minimumY, maximumY);

         transform.localEulerAngles = new Vector3(-rotationY, rotationX, 0);
     }
     else if (axes == RotationAxes.MouseX)
     {
         transform.Rotate(0, Input.GetAxis("Mouse X") * sensitivityX * Time.deltaTime, 0);
     }
     else
     {
         rotationY += Input.GetAxis("Mouse Y") * sensitivityY * Time.deltaTime;
         rotationY = Mathf.Clamp(rotationY, minimumY, maximumY);

         transform.localEulerAngles = new Vector3(-rotationY, transform.localEulerAngles.y, 0);
     }
     if (lockCursor)
     {
         Cursor.lockState = CursorLockMode.Locked;
     }


     //transform.Rotate(Input.GetAxis("Mouse Y") * new Vector3(sensitivityY, 0, 0) * Time.deltaTime);

     if (lockCursor)
     {
         Cursor.lockState = CursorLockMode.Locked;
         
     }
     
     

 }

   
 

} `