>>59020892iirc, Ditto copies its target and whether or not it's shiny, regardless of whether or not the Ditto itself is shiny.
This is why when you see a transformed Ditto's sleep style, you don't see if it's shiny until it wakes up for feeding time.
Pokémon Go operates like this as well. When it first debuted, Ditto's disguises could be shiny whilst the Ditto itself was not shiny, and this was corrected so that its disguises would never be shiny as to avoid disappointing players.
On a similar note, wild Zorua disguises itself as your buddy in Pokémon Go; including if it's shiny, has a costume, or if it wears the Best Buddy ribbon.
If Zorua and Zoroark were ever introduced to Sleep, they could implement a gimmick where its own sleep style mimics someone in your sleep team; maybe just the team leader.