What action does “打” in “打酱油” refer to?
打 in 打酱油 doesn't intrinsically mean "buy". In the last century, soy sauce was not sold in bottles as today. It was produced by the merchant himself, so you need to go to the shop and ladle it into your container from a big jar. 打 is for the action to lift liquid from a jar or well with long spoon / bucket etc. SO IT DOENSN'T MEAN “BUY” ELSEWHERE.