Three parts of the Temptation of the Mothbinder set are not seen as part of the set by the game.

When viewing the set in the shop, it shows only 3 of the 5 parts as a set, and lists the other 2 parts as individual items.

When trying to equip the set via the list of full sets you own, it only equips the hood, skirt and bracelets of the set, and you have to equip the armor, belt and spirits manually afterwards.