How can I calculate the velocity of an object that moves with drag and drop controls ?

Does the object use a rigidbody? If so, you can just get the velocity of the rb OnRelease, through rb.velocity.

If not (assu$$anonymous$$g it's just manually setting the transform), you can save the last position, and subtract it from the current one, every frame, to calculate the velocity (or change in position over time). For example:

 Vector3 lastPos;
 
 void Update()
 {
      // Dragging logic here
 
      Vector3 velocity = transform.position - lastPos;
      Debug.Log(velocity);
 
      lastPos = transform.position;
 }