I promise I was more laughing at the idea of "Chef" being a Feat than I was at you for not knowing something so specific about a game you do not play. I should have copy-pasted it into my post; I apologize.I didn't know that 5e D&D has a Chef feat until you mentioned it. I just Googled it and learned that, in addition to the WIS boost you mentioned, it gives a way of healing hp, a way of granting temp hp, and proficiency in cooking utensils.
It doesn't seem to tell us anything about whether or not the character should do better in a cooking competition than another character without the feat. That would be something the GM would just have to decide, I guess.
I agree that if a cooking competition of some sort emerges from play in a 5E game, it would be up to the DM to figure out how to run it. One can either look at it as the game doesn't have specific rules for it, so there's no support; or one can look at it as there's a framework to base adjudication on, so there's plenty of support. It should not surprise you that I lean toward the latter.