Limit gameobject rotation to -480 and 480 degrees?

It's slightly more involved to handle larger angles, but not *THAT* bad. Rather than worrying about absolute angles, you can instead handle relative angles.

Using the linked script as a template, I made a few adjustments:

 using UnityEngine;
 
 public class ClickDragRotate : MonoBehaviour
 {
     public float minAngle = -480;
     public float maxAngle = 480;
 
     float angle = 0;
     float lastAngle = 0;
 
     void OnMouseDown()
     {
         Vector3 pos = Camera.main.WorldToScreenPoint(transform.position);
         pos = Input.mousePosition - pos;
         lastAngle = Mathf.Atan2(pos.y, pos.x);
     }
 
     void OnMouseDrag()
     {
         Vector3 pos = Camera.main.WorldToScreenPoint(transform.position);
         pos = Input.mousePosition - pos;
         // 2D rotation matrix to undo the current rotation
         // [cos(T) -sin(T)]
         // [sin(T)  cos(T)]
         Vector3 rotatedPos = new Vector3(pos.x * Mathf.Cos(-lastAngle) - pos.y * Mathf.Sin(-lastAngle), pos.x * Mathf.Sin(-lastAngle) + pos.y * Mathf.Cos(-lastAngle), 0);
         float currentAngle = Mathf.Atan2(rotatedPos.y, rotatedPos.x);
         angle += currentAngle * Mathf.Rad2Deg;
         lastAngle = Mathf.Atan2(pos.y, pos.x);
         angle = Mathf.Clamp(angle, minAngle, maxAngle);
         transform.rotation = Quaternion.AngleAxis(angle, transform.forward);
     }
 }

I save the last frame's angle, then use that to rotate the current frame's position vector backward. At that point, Atan2() can be used safely without (usually) worrying about the -180/180 degree boundary. Once I have that new angle for the current frame, I simply add that to the current total angle and clamp it between the defined minimum and maximum angles.