Carbink's attack stats are pretty bad, so it wouldn't be my first choice. However, against the League, its STAB moves can hit two of Acerola's team super effectively, along with Kahili's entire team, and a good chunk of of Hau's team. There are better Rock and Fairy types out there, though, so I really wouldn't recommend Carbink for in-game play. But it of course works, as does everything ingame.
As a Pokemon designated to catch other Pokemon, Carbink is not too good, as you have things like Absol that work better. It can learn Skill Swap, so if you're trying to catch a Pokemon with an Ability that you don't want on it while you try to catch it, that could be an option. It doesn't learn False Swipe or Thunder Wave, so it's not good in that regard either. Overall, not a good Pokemon to catch others with.
Bear in mind I don't know a lot about Gen 7 competitive, but I could see this thing as a Screen Setter, with access to both Light Screen and Reflect. Give it a Light Clay to prolong the Screens, and your teammates can put in work. It learns Hail, Sandstorm, and Sunny Day, so it could be a really bad weather setter. It can also set up Stealth Rock, to cripple opponents. it can also learn Trick Room, but there are better TR setters.
In conclusion, Carbink isn't a very good Pokemon at, well, anything. It can work, but not as well as other things.
Hope I helped, and congrats on the shiny!