How to set screen boundaries on a moving camera

Thanks in advance to anyone who replies.

I am working on a basic horizontal shooter game where the screen moves horizontally at a fixed rate whilst the player moves around the screen shooting at incoming projectiles. My problem is that I have set the screen boundaries using the ScreenToWorldPoint; however after the camera moves a certain distance my player object is being pushed outside of the screen space.

Please find my code attached below. It might help clarify the issue:

 using UnityEngine;
 
 // Attached to the player
 public class ScreenBoundaries : MonoBehaviour
 {
     private Vector3 screenBoundaries;
     public GameObject player;
 
     private void Start()
     {
         SetBoundaries();
     }
 
     private void Update()
     {       
         Vector3 playerPosition = player.transform.position;
         playerPosition.x = Mathf.Clamp(playerPosition.x, screenBoundaries.x, -screenBoundaries.x);
         playerPosition.y = Mathf.Clamp(playerPosition.y, screenBoundaries.y, -screenBoundaries.y);
         player.transform.position = playerPosition;
     }
 
     private void SetBoundaries()
     {
         screenBoundaries = Camera.main.ScreenToWorldPoint(new Vector3(Screen.width, Screen.height, 
         Camera.main.transform.position.z));
     }
 }