The EU has already defined dairy items milk, butter, cream, yoghurt and cheese as "products secreted by mammary glands", meaning that what might otherwise be called oat milk is instead generally referred to as oat drink.

Meanwhile, back in 1755:

MILK. n.s. [meelc, Saxon; melck, Dutch.]

2. Emulsion made by contusion of seeds.

Pistachoes, so they be good and not musty, joined with almonds in almond milk, or made into a milk of themselves, like unto almond milk, are an excellent nourisher.