change objects Axis to match cameras rotation

So i am making a simple game at the moment a platforming one and i am working on the camera. so far i have been able to get the camera to follow the player as well the camera being able to move left and right with the mouses X axis. now the only issue i am having is trying to figure out how to match the objects axis with where the player is looking since when i turn the camera around pressing "W" will still make the object go the same direction. what i want it to do is the objects axis should follow where the camera is looking so if i go forward and switch my camera position the object should be going forward in respect of where the camera is looking

 using UnityEngine;
 
 public class Follow_Player : MonoBehaviour {
     public Vector3 offset;
     public Transform Player;
     public float turnspeed = 4.0f;
     
     
     // Update is called once per frame
     void Update () {
         transform.position = Player.position + offset;
 
 
     }
 
 
  
 
     private void LateUpdate()
     {
         offset = Quaternion.AngleAxis(Input.GetAxis("Mouse X") * turnspeed, Vector3.up) * offset;
         transform.position = Player.position + offset;
         transform.LookAt(Player.position);
 
         
 }

this is the code for the camera which allows it to follow the player as well as allowing it to rotate on its x axis if someone can help me on how to make the axis match where the camera is looking or at least explain that would be wonderful thanks!