Drag object on XZ with perspective

Hi all! A bit of a noob here in Unity, I couldn't find quite what I'm looking for this.

I have a plane (viewed at an angle) and an object that falls gradually above it, like a 3D tetris.

I want to touch anywhere on the screen and drag the object on its XZ axis (the falling on Y axis happens automatically).

Left-Right movement works ok, but the Forward-Backwards movement (towards and away from the camera) is too slow (eg. moving my finger 1cm horizontally moves the object 1cm left-right, but moving it vertically the object only moves 0.2cm forwards or backwards)

How can I make it so that the movement is uniform in any direction?

For now this is what I have in my LateUpdate (or should that be in Update? ):

     private bool dragging = false;
     float posX;
     float posZ;
     float posY;
 
 void LateUpdate()
     {
         if (Input.touchCount > 1)
         {
             return;
         }
 
         if (Input.GetMouseButtonDown(0))
         {
             Vector3 dist = Camera.main.WorldToScreenPoint(transform.position);
             posX = Input.mousePosition.x - dist.x;
             posY = Input.mousePosition.y - dist.y;
             posZ = Input.mousePosition.z - dist.z;
 
             dragging = true;
             return;
         }
         else if (Input.GetMouseButtonUp(0))
         {
             dragging = false;
         }
 
         if (dragging)
         {
             float disX = Input.mousePosition.x - posX;
             float disY = Input.mousePosition.y - posY;
             float disZ = Input.mousePosition.z - posZ;
             Vector3 newPosVector = new Vector3(disX, disY, disZ);
             Vector3 lastPos = Camera.main.ScreenToWorldPoint(newPosVector);
             transform.position = new Vector3(lastPos.x, transform.position.y, lastPos.z);
         }
     }

Thank you!