Rotate point on XY plane to face object

I realize there are a million threads on this topic but I cannot figure this out.

I am working on the 2D XY plane with Z being depth. I want to rotate an object to face a point (both instantly and over time but let's focus on instantly). I have tried my own version and many online and all either fail catastrophically (spasming) or not rotating on the correct axis.

I want the rotation to act as though there are only 2 dimensions. Its a top down shooter like this and this. What do I need to do?

I've tried

         Vector3 mouse_pos = Input.mousePosition;
         mouse_pos.z = 30; //The distance between the camera and object
         Vector3 object_pos = Camera.main.WorldToScreenPoint(gameObject.transform.position);
         mouse_pos.x = mouse_pos.x - object_pos.x;
         mouse_pos.y = mouse_pos.y - object_pos.y;
         float angle = Mathf.Atan2(mouse_pos.y, mouse_pos.x) * Mathf.Rad2Deg;
         gameObject.transform.rotation = Quaternion.Euler(new Vector3(0, 0, angle` - 90));

and

         target = v;
 
         float adj = (gameObject.transform.position.z - v.z);
         float opp = (gameObject.transform.position.x - v.x);
 
         float cot = Mathf.Atan(opp/adj) * Mathf.Rad2Deg;
         
         cot *= -1;
         if(v.z > gameObject.transform.position.z){
             cot-=180;
         }
         gameObject.transform.Rotate (new Vector3(0,0,cot));