In the tosfos on hachonoh. The first answer to the kashia on Rashi from eiruv tavshilin is that the hachonoh of hoilodas beitzah is more chomur than that of affiah and bishul so the latter is only d'Rabonon. Does that mean that possuk that both Rashi and Tosfos qoute for affiah and bishul is for the issur min haTorah on Shabbos or is it for some other aspect of hachonh/muktzeh?
If you are referring to the Pasuk of "Es Asher Tofu Efu" (Shemos 16:23), it seems from Rashi that it is coming to prohibit cooking/baking on Shabbos, as you say. Maybe it is adding a Mitzvas Aseh for the preparation of food for Shabbos, besides the Isur of cooking on Shabbos. For this reason, Chazal tell us (Kidushin 41a that when preparing for Shabbos, the rule "Mitzvah Bo Yoser mibi'Shelucho" dictates that one should do it himself.
In either case, it would not be related to Hachanah; nor does the Pasuk mention Hachanah there.
Be well, Mordecai