I don't think we see any actual Stormtroopers operating the controls on the bridge of a Star Destroyer. There are plenty of officers and technicians operating controls, but what Stormtroopers (white armor) we do see seem to be guarding halls and doors.
As for what the bridge officers and technicians are doing, they do what bridge officers for any large vehicle do:
- Interpreting instrumentation for commanders as a commander can't look at all the screens.
- Expanding on commanders orders and relaying them to appropriate departments or sections of the ship.
- Managing departments or sections of the ship.
- Coordinating Stormtrooper movements within the ship and on the ground (in event of ground action).
- Managing fighter readiness and tracking friendly fighters.
- Direct weapons fire from the many weapons batteries, the more weapons stations the more independently each weapon can fire.
Ships are typically broken into departments: Engines, maneuvering, navigation, weapons, tractor control, flight deck, communications (long range, short range, ground forces), shields, life support, etc. The more fragmented the departments the more they can work independent of each other and be more specialized in their command.
In each "crew pit" we see 8 stations with an officer observing. Plus console alcoves flanking either side of the bridge as well as stations implied at the rear. From screenshots and gaming material places the bridge layout as 12-16 consoles in the "crew pits" plus 2-4 officers. Flanking bays have a total of 1 to 3 consoles each plus an officer for each bay. Then 2-6 consoles in the rear bay with corresponding officers. That would put the bridge crew around 14 to 30 technicians and 6 officers not including commander and second.