Question About Basic Supply/Demand Concepts
You are right that most discussions talk about complementarity in consumption, which is why this question is all the more interesting.

Demand falls for potatoes, which causes the price of potatoes to fall, which causes the supply of potatoes to fall. This means there is less starch available. This in turn means that we can make less packing-peanuts, hence supply of packing peanuts falls.

You are right that demand for packing peanuts does not change. The supply will nevertheless change however. This is because the supply of starch falls and the input factor of packaging peanuts is more expensive, so less is optimally produced. I.e. the supply curve of packaging peanuts changes, in this case shifts to the left so there is less equilibrium supply even though demand for packaging peanuts has not changed.