This whole thing is so absurd… the copper mug thing is a result of someone having leftover copper mugs that they couldn’t figure out how to move, and they paired with the vodka people, who couldn’t figure out how to sell vodka.
They adapted a category of drink called a “Buck”, which was spirits, lime/lemon and ginger beer, with vodka, served it in the copper mugs, and called it a “Moscow Mule”. The combination took off because it’s tasty, and it’s attention-grabbing with the copper mugs.
But it’s nothing special; the “buck” category long predates the Moscow Mule. Whiskey bucks haven’t ever been uncommon for example, and a specific sort of rum buck has its own name- the Dark and Stormy.