If it makes you feel any better the milk, and all the foods you eat, already contain micro-plastics 👍

Paper stuff that is meant to hold liquids will always be just a plastic bag with carton structure. Wax would be fine if you were filling and storing the liquid in your own home. But wax lined paper would never survive the shortest of transportation. Completely non-feasible for industrial scale agriculture. Soft drinks in cans also have plastic linings, metals are more resistant but would also eventually corrode in the midterm.