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 Harris's hawk formerly known as the bay-winged hawk or dusky hawk, is a medium-large bird of prey that breeds from the southwestern United States south to Chile, central Argentina, and Brazil. Birds are sometimes reported at large in Western Europe, especially Britain, but it is a popular species in falconry and these records almost certainly all refer to escapes from captivity. The name is derived from the Greek para, meaning beside, near or like, and the Latin buteo, referring to a kind of