So I did not watch this documentary to the end (I believe it follows a German dude who thinks Carthaginians discovered the Americas). But here is a nice 2-second segment with a slinger-- clearly a modern Balearic dude with a braided sling (the pouch is reinforced with leather), and wearing a goat skin and headband sling to look ancient, perhaps a reenactor. Good style, too, with the released end wrapping around the body

https://youtu.be/hbEShcMz-Fc?t=174