The thickness and depth are part of the backsplash, however, I am not sure what do you mean with Back, Left and Right depth?. Do you mean Back, Left and Right visibility?

In the image below you can see a base cabinet with the backsplash (in green) and the countertop (in red). In this case, I set the back and right viability for the backsplash.

When you set a counter top, you can customize the Thickness as well as Front, Left or Right Overhang.

When you set a backsplash, you can customize the Height, Depth as well as Front, Left or Right Visibility