having a dilemma with a canShoot bool in an fps

Instead of disabling your gun on pause, disable the UI Buttons or key presses that can shoot, or change them to something that can't be pressed. This will prevent any hassle or debugging issues later.

Why don’t you setup some events instead of checking every update call?? Pause game can Invoke() an event that tells listeners it is not paused and you only set your shooting bool true when the event is triggered not every update.

 [System.Serializable]
 public class MyBoolEvent : UnityEvent<bool>
 {}
 
 public class PauseClass : MonoBehaviour
 {
     public MyBoolEvent isPausedEvent;
 
     [SerializeField] private Button pauseButton;
     
     private bool isPaused = false;
 
     private void Start()
     {
         if(isPausedEvent == null)
             isPausedEvent = new MyBoolEvent();
 
         pauseButton.onClick.AddListener( ( ) =>
         {
             isPaused = !isPaused;
             isPausedEvent.Invoke( isPaused );
         } );
     }
 }
 
 public class ShotgunClass : MonoBehaviour
 {
     [SerializeField] private PauseClass;
     
     private bool canShoot = true;
 
     private void Start()
     {
         PauseClass.isPauseEvent.AddListener((bool pauseStatus) => 
         {
             if(pauseStatus)
                 canShoot = false;
 
             else
                 canShoot = true;
         } );
     }
 }

You should set it up so none of the code for your player runs while the game is paused.