The brake pedal should be directly attached to the output rod of the booster, so should be no play there. The spring in the booster will move the pedal back until it reaches an internal stop in the booster. That should determine where the pedal sits with your foot off. It should not bottom out on the brake lamp switch.
The MC also has a return spring and an internal stop. You want that to exactly match the booster's output rod, with negligible gap, if any. Too much gap and the pedal will have excessive lost-motion, as you experience. In worst-case, the pedal could bottom out on the car's floor, to limit braking ability. If the output rod is too long, it can prevent the MC piston from coming back enough to expose the fill port. That causes "hydraulic lockup". Do you also have that? That means that the brakes never release, especially after driving and using them a while so the brake fluid expands slightly due to heat.
Regardless, most output rods have an adjustable tip. You need a special tool to measure and adjust. I bought a $15 plastic one on ebay. But, it wasn't quite right for the base feet to fit over the MC protrusion on one of my vehicles. Should work on your MC if that flange is smooth. Watch youtubes. The lost pedal motion might be air in the system rather than a large gap between MC piston and booster rod. Bleeding thru new fluid is the fix for that.
