This is a tiny mod that just alters the tuning ID for the four base game closet shelves to make them functional. There are functional versions of these out there, but not as default replacements.
As an added bonus, because these only affect the object definition, not the catalog, they aren’t seen by the game as being custom objects. Exact same price and catalog location as the originals, under Decorations / Wall Sculptures for §160 each, or can be found quickly by searching for “closet” in-game. The four items replaced are “Wall-Mounted Coat Rack With Shelf”, “Another Wall-Mounted Coat Rack With Shelf”, “Yet Another Wall-Mounted Coat Rack With Shelf” and “Shelf Storage Unit With Hangers”