While the Army has the reputation of maintaining records of all kinds through its history, sometimes that reputation gets stretched over time. While the Army may have kept track of the most expensive item issued to Civil War-era soldiers, their rifle musket, individual uniform items would not have been accounted for in that fashion. Issued uniform items and equipment were considered expendable items and were lost in prodigious numbers (your discovery of the belt buckle is good evidence), so strict accountability for such issue items would have been a serious waste of time for the regimental quartermaster.
The number on the back of the buckle would have been of use to the buckle manufacturer or perhaps to the Army inspector receiving a shipment of buckles on behalf of the Government, but no more than that.
I hope you find this information helpful.