This doesn't seem to be a function in the Ultimate Collection, or at least I don't know how to enable it. Can anyone help?

That's a function that came with Seasons, I think, so it should be part of the UC and already enabled. To store leftovers, you would click on the plate or platter of the leftovers and select putaway leftovers from the menu. Not sure if that's the exact wording at the moment but the menu option is something similar. If you're trying to store leftovers of a cake, you can't store the whole cake, only the individual slices. If you're not getting the option, it may be that you have a mod to stop it. I haven't seen any mods that adds the feature

You can totally store a whole cake as leftovers.

Do you have a custom fridge? If you have a custom fridge that wasn't updated for the storing leftovers function then it won't have the option.

It is in the UC - it is probably the fridge - like Charity says. If you download a fridge or a kitchen, many creators do give a choice between base game and free time ones. Sometimes they are both in the download and you have to remove the one that is not suited to your game.

Gotta check out my mods folder, then. Thanks, everyone!

Kind of off topic, but how? I never get the option to store leftovers on a whole cake. Though I only use birthday cakes. Would that make a difference?

You can't store the birthday cake, only those you bake.

Yeah, only baked cakes.