I found it difficult to answer your question of whether the generation of a menu of different dishes from a given number of ingredients came from a restaurateur/commercial cook or from a domestic cook.
Historians may or may not agree with me that supportive evidence with a reliable date stamp (not a novel of fiction), as searched back to the year dot, is hard to find or even non-existent, given that there is a probable general lack of that level of documentary evidence.
Given necessity is the mother of invention, if you were the army cook in a besieged garrison, you would have to very soon (say, between meals !!) figure out this “new” menu to feed your troop…..or in times of famine, any cook (worth his/her weight in salt !!!) using limited resources of ingredients, whether in a domestic or commercial situation, would have to very soon arrive at this solution.
So my comment is open, and above all, “let us eat and be merry” !!!