One way to picture starchy: think of a white powder. Stirred into food, it makes soup thick and fills you up fast. Brushed onto cloth and dried, it makes a shirt flat, smooth and hard, so the collar will not bend. The word walks along that one picture: food that holds a lot of the powder, cloth that has been treated with it, and finally a person who behaves like that cloth — neat, correct, and impossible to bend.
From the word’s history
Wiktionary gives the word as starch + -y, that is, having starch in or on it. That simple shape is what lets one word cover food, cloth and manner.
Wiktionary 記的是 starch 加上 -y，也就是「有澱粉／有漿的」。字的結構這麼直白，所以食物、布料、舉止三個方向都能共用同一個字。
packet Wiktionary etymology_text for starchy (kaikki:3f6f69a190036ae4:1270632949:12277): From starch + -y.
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