I'll answer this more in-depth in an hour or so, but the straight answer now:
Military-issue NSPs have the grenade-like function on them, as well as automatic fire. The SAoY takes the NSP from the soldier when they retire/leave the service/whatever and can either reissue it (common with Type 28As and Cs) or modify it for a civilian-grade version (remove the grips from the Cs, but keep the military finish, along with the remove of auto-fire and grenade).
Since the SAoY owns the equipment given to the soldier, they get to take it back at the end. If shit goes missing, there's probably a consequence of some sort, though whether it's anything serious or not is hard to gauge.
Some military-grade NSPs probably made it to Nepleslia, but they're likely to be the old Type 28s, not the 28As or Cs. It's also theoretically possible to modify a civilian-grade NSP with the right know-how and parts. The Type 27s, oddly enough, are harder to find, as many older Nekovalkyrja keep them.
The older weapons are be sold by shops on Yamatai, but military-grade is for military only.