You have a groundspeed greater than that of the speed of sound, correct.
However, you are not supersonic.
For speed of sound and figuring out if you are supersonic or if the airflow over any part of the aircraft is supersonic the only thing that matters is the relative speed of the aircraft/part of the aircraft and the air. The ground has nothing to do with it all. So while your GS is great than LSS it has no significant impact on the operation.