Actually, most guns marked U.S. PROPERTY still went to the Navy. That stamping replaced US NAVY after the Army Supply Program took over the contracts, but that didn’t change their primary military use by the Navy.

However, the Navy generally did not issue these as personal sidearms, only for duty, like dockside guards, or pilots before they took off for a mission, to be turned back in afterwards. So while it’s possible, it is unlikely that the gun and holster spent the war together.