Camera follow the player code

I am trying to get the main camera follow the player movement. Here is my code to do so: *The playerController :

 // Start is called before the first frame update
 void Start()
 {
     directions = new Dictionary<KeyCode, Vector3> {
         {KeyCode.W, Vector3.forward},
         {KeyCode.S, Vector3.back},
         {KeyCode.A, Vector3.left},
         {KeyCode.D, Vector3.right}
     };
 }

 // Update is called once per frame
 void Update()
 {
     foreach (KeyCode direction in directions.Keys)
     {
         if (Input.GetKey(direction)) {
             this.transform.Translate(directions[direction] * speed * Time.deltaTime, Space.Self);
             Debug.Log("Character is moving");
         } 
     }
 }

}

*The cameraController:

 public class CameraController : MonoBehaviour
 {
 public Transform target;
  
 public Vector3 offset_move;

 void Start() {
     offset_move = transform.position - target.position;
     Debug.Log("offset" + offset_move);
 }
 void Update() {
    
 }
 void LateUpdate() {  
     transform.position = target.position + offset_move;
 }
 }

With this code the camera position is changing but it seems that the camera isnt following the player. Can someone point out what i did wrong and help me fix this?