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.
Bird animal totems have been used symbolically within all cultures throughout history. In the true sense, specific animal instincts and characteristics represent the qualities that we humans should learn to emulate. However, because we lead such busy and complicated lives, often there is no time for self-reflection.