I’d recommend adding some Debug.Log statements to your code, so you can make sure the code is being called.
Looking at this again, though, I’m not sure your logic makes sense. It seems like this code would keep adding to the camera’s position even if you weren’t moving the mouse. Two approaches would be to set the position to direction, not add direction to it. Or, keep track of the last position (instead of touchStart) from the last frame, and do the delta based on that.
You’re also translating the XY 2D position of the mouse to 3D position. Are you sure that’s what you want? I’d think you might want to change the camera’s XZ values based on the mouse movement’s XY value.