That's a nice find. I wonder why, tho, it looks like it is two piece from the back. Obvi I found other pics online, and those are more evident. Saw something about the 76th being called MacDonald's Highlanders Started in 1777, but landed in NY in 1779.
It's the plating wrapping around the edge of the button that makes it look like a two piece.
Yes MacDonald's Highlanders and they basically just fought in the war and then disbanded.