>>48373677it’s a reference to The Red Shoes by Hans Christian Andersen,
especially the nubbed amputated feet.
Basically a girl wears red shoes to church and is subsequently cursed to dance forever in them. An angel condemns her to dance even after death, then she amputates her feet and the shoes dance away on their own. After the girl prays to God she dies and goes to heaven where people pretend to not know about the shoes.
That’s why it changes into a dancing mode, and that’s why missing red shoes are mentioned in the dex entry. Maybe if the BW Anime plot wasn’t shelved there would have been a little more explanation, iirc Meloetta showed up there so they didn’t make a movie.