Food prices in general tend to follow hydrocarbon prices. Not just because of the tractors and trucks, but also because of fertilizer. The Haber process is essentially a method of turning natural gas into corn and wheat (and then beef, pork, etc.)

Something like 5% of world natural gas consumption is to drive the Haber process to create fertilizer that then drives everything else in modern agriculture. Now, natural gas and oil prices are not as correlated now as they used to be (due to fracking) but there seems to be some residual connection between the two, so that could be something to look out for.

In the USA, oil represents about 17% of manufacturing pricing. It obviously hits some industries much harder than others. Agriculture is particularly vulnerable. Large-scale farmers have tight margins and fertilizer is essential to factory farming.

Food prices rise and fall with oil.

That’s probably it.

Nothing much. Cost of liquid fuel is not the constraint on economic activity in the developed world.