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 sankofa bird appears frequently in traditional Akan art, and has also been adopted as an important symbol in an African-American and African Diaspora context to represent the need to reflect on the past to build a successful future. It is one of the most widely dispersed adinkra symbols, appearing in modern jewelry, tattoos, and clothing.