Learn English – Word for “food eaten only partially out of hunger”

To stay one's hunger is perfectly acceptable, and not at all uncommon (though it's actually more likely to be "stay your appetite"). Less common, and with less of a "temporarily" sense, would be assuage one's hunger. But I think probably the most common idiomatic usage is...

Here - have a sandwich to stave off your hunger until dinnertime.

...which my mother used to say to me when I was a child. Perhaps this one gains traction by alliteration / association with both stay and starve.

to stave off
to fend off, to ward off (something adverse) _{Merriam-Webster}

(To metaphorically repel / drive away using a stave = staff = stick.)

You might want to ask this kind of question on Seasoned Advice, the Stack Exchange site for cooks.

The way to describe all the ingredients, in the state of having been purchased, cleaned, trimmed, cut, etc., is to say that they have been prepped (short for prepared).

A person in a restaurant kitchen that does nothing but clean, trim, etc is called a prep cook, and they work at a prep station. When working with a chef, one might say:

Do you need me to prep the vegetables?