MAYBE…try reading your own product descriptions on the front page?
•Made of nickel-lined Solid Copper with solid brass handles
•Tarnish-resistant clear finish over the copper for lasting beauty and luster
•Beautiful solid copper construction with tin lining and solid brass accents
•The tarnish resistant lacquer coating preserves beauty and luster
•This set of 4 Moscow Mule mugs are made of nickel-lined Solid Copper with solid brass handles
•These sturdy mugs feature a tarnish-resistant clear finish over the copper for lasting beauty and luster
So you are drinking from anything but copper.
Tin shows chemical similarity to both germanium and lead
You can be exposed to Nickle just by breathing air and for the most part it is found in food, water, air, etc and Will pass through your urine. It is also used to make stainless steel. I’d be less concerned about the nickle lined mugs.
The Tarnish-resistant finish (lacquer) is not healthy and will wear off quickly. So hope for a quick poison and recovery.