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 Golden Peacock. Birds are songsters, and, unsurprisingly, there are lots of songs about them in Jewish â if not most â languages. They are magical beings, mediating between heaven and earth, embodying our desires to fly free from the chains of mundane experience and to reach spiritual heights.