Whether they have any extant function or not, they have lost their former function and in that sense they do fit the definition of vestigiality. Vestigial structures are often called vestigial organs, although many of them are not actually organs.
There are quite a few birds famous for doing ritualized mating dances, so I would only list 5: The Red Capped Manakin, The Black-footed albatross, The Western and Clark's grebe, The Superb bird of Paradise, & The Victoria's riflebird.
The law designating the mountain bluebird (Sialia arctcia) as the official Idaho state bird is Section 67-4501 (STATE BIRD DESIGNATED) of the Idaho Statutes, Title 67 (STATE GOVERNMENT AND STATE AFFAIRS) Chapter 45 (STATE SYMBOLS) Section 67-4501.