Addbags[configs_List] :=
 DeleteDuplicates[
  Map[LexicographicSort,
   Catenate[AddbagAll /@ configs], \[Infinity]]]
AddbagAll[config_] :=
 Addbag[config, #] & /@ Position[config, bag[___], \[Infinity]]
Addbag[config_, pos_] :=
 ReplacePart[config, pos -> Append[Extract[config, pos], bag[]]]
With[{n = 5}, Nest[Addbags, {cabinet[bag[]]}, n - 1] // Column]