So even though a simple meal might literally cost $2–$3 in raw ingredients, the delivered price after contracting can be way higher.

When DFACs get contracted out to companies like Aramark, Sodexo, etc., the government ends up paying contractor prices, not “cost of ingredients + labor.”
Those companies need profit margins, management overhead, and contract compliance teams all of that gets baked into the cost.

It's nice having a holiday