That's been the term of choice in English for the past 800+ years

In English, the word "milk" has been used to refer to "milk-like plant juices" since 1200 CE.[11]

Plant milks go back much further than most people realize

Almond milk spread throughout Europe during the Middle Ages and was popular in parts of the Middle East. Recipes for almond milk in the Middle East date back to around the 13th century as it was mentioned in Muhammad bin Hasan al-Baghdadi’s cookbook Kitāb al-Ṭabīḫ (كتاب الطبيخ; The Book of Dishes), written in 1226. It was especially popular during Lent.[12][13][14][15] Soy was a plant milk used in China during the 14th century.[3][16] Soy milk use in China is first recorded in 1365.[17] In medieval England, almond milk was used in dishes such as ris alkere (a type of rice pudding)[18] and appears in the recipe collection The Forme of Cury.[19] Coconut milk (and coconut cream) are traditional ingredients in many cuisines such as in South and Southeast Asia, and are often used in curries.[20]

https://en.wikipedia.org/wiki/Plant_milk

Some of them are sold as " drink", though these seem to contain quite a bit more sugar than milk alternatives branded as " milk".