In my opinion (as with anything I say) with regard to the Jewish people it is both.
For instance in the first siman in chelek gimmel of the Mishnah Berurah in the last sif (I forgot which it is) the Hagah (may have been the mechaber- I have a bad memory)writes that there is a minhag to eat a “pashtidah” as a zecher for the man. I don’t remember if the Shulchan Aruch says it or the Mishnah Berurah, but it is explained that it has a top and bottom layer of dough with meat in the middle. The Mishnah Berurah writes that in his days it is still the minhag.
So I would argue that at first there was probably no minhag to eat this “pashtidah” at all. In Europe these types of foods were common and soon people were eating them on Shabbos. But ve’amech kulam tzaddikim, nothing we do is just stam so we found a way to add a mitzvah to this ordinary food and it became a minhag. Similar to how some people have a minhag to eat kishke potato kugel apple kugel and lukshen kugel since in Yiddish it spells Amalek. Or making yihi ratzon on Rosh HaShanah for foods based on their yiddish names.
In my opinion nothing the klal takes on can be just stam. We are under Hashgacha Klalis and we are too holy as a unit. Just like a tzaddik doesn’t raise his finger without kavana lishem shamayim the klal as a whole does not move with out kavana lishem shamayim.
That is my personal opinion on this, but I definitely see a lot of room to disagree with me.