How to automatically add a script component to a generic gameobject in the editor?

So, I am working on this game, and I am supposed to make a system to change level based on Triggers the player enter. I have a singleton with a list of classes, each class is a trigger to add on the current level. This is the Trigger Class:

 [System.Serializable]
     public class TriggerClass
     {
 
         public GameObject Trigger;
         public bool Active;
 
         public TriggerClass(GameObject obje, bool active = false) //constructor
         {
             Trigger = obje;
             Active = active;
         }
     }

And the list:

 public List<TriggerClass> Triggers = new List<TriggerClass>();

As the OnTriggerEnter() callback must be called on the trigger object, there need to be a script attached to every single trigger gameobject, whatever the trigger is, that I called TriggerScript. Considering that in the Inspector it shows that pretty system with the Triggers List, where you type in the size and it automatically creates the elements, is there any way that I could make the TriggerScript automatically attach to the object when the artist just drags it into the gameObject field in the list element?