Rotate object permanently around Y-axis while rotating around Z-axis to face mouse?

I'm working on a 2D game and I'm trying to make an object rotate around the Y-axis permanently while having it face the mouse using its Z-axis rotation - like a side view of a fidget spinner on a finger.

         float zCam = -Camera.main.transform.position.z;
         var mouseVector = new Vector3(Input.mousePosition.x, Input.mousePosition.y, zCam);
         var mPos = Camera.main.ScreenToWorldPoint(mouseVector);
 
         var lookPos = mPos - transform.position;
         lookPos.z = 0;
          float rotationZ = Mathf.Atan2(lookPos.y, lookPos.x) * Mathf.Rad2Deg;
 
          transform.rotation = Quaternion.Euler(0.0f, 0.0f, rotationZ);
 

This is my current code, but I can't get the object to rotate permanently around the Y-axis using this code! Can anyone help?

Edit: I should mention it's a 2D game with 3D objects - hence the rotation