"cooper" derives from the verb "coop", which likely derives from Latin "cūpa", from which we get the word "cup".

Perhaps (citation needed)! Barrel usage in Britain is a lot older than the Roman occupation of Britain. A cup is not a barrel.

If I was to bet, cooper is probably an anglicized form of a brythonic language word. Any Welsh, Scottish, Irish, Cornish or even Cumbric (int al) speakers hanging around here?