There’s no such animal. Purple birds are a color anomaly or hoax.
The Woodhouse Eurasian Jay article writes “Birds do not produce true blue plumage, so the bird is either an immature bird still in its first year and has yet to grow its final adult feathers -or- it is a hybrid Cross between the blue European Jay (C.garrulus) and one of the Oriental Jays (Cinnyris). The only possible exception might be if this bird was found in isolation on some remote island.”
The European Blue Tit normally changes from brown to green in late autumn while immature, before changing again into their new white winter dress at about 6 months old. But Boesman beautifully illustrated how spectacled caucasus titmouse A. maurus undergoes a color change on its own, from brown to blue in winter.