1920 luger carbines were made from left over part during the Weimer period, See Land of Borchardt! '1920 carbine' often referred to as the "Parts Carbines" Your assumption is correct as to the prior 1902 carbine! The serial# is 3231t and its all matching and proofed~ '31' through out~
https://www.landofborchardt.com/lugerads.html see 1920s A 'New Model Parts Gun'