2what it changes
The extra accessory slot is the single biggest power jump Expert Mode hands you, larger than most of the gear you find around the same point. Plan for it. It arrives exactly at the Hardmode transition, so the movement accessory you were about to shelve for a damage one can stay on instead.
It attaches to the character, not the world, and a second one does nothing. Once you have used one, later treasure bags stop producing them, so there is no stock to hoard and nothing to trade.
classic worlds
Take the same character into a classic world and the slot goes dark. Whatever sits in it stops working, and you cannot put anything new there, though you can pull the old item back out. The one thing that leaks through is fall damage immunity from wings, which stays with you across the boundary.