To store it on a hard disk, it would take roughly 1.32375 GB to store the information on each of the 8 datacenter for all created characters separated equally between them. Assuming each gear item ID on the lodestone only require 1 bit as a flag to know if you ever owned the item or not.

No idea how much additional bandwidth it would cost to send it back and forth from the server to the player each time they log in or load an instance.

This doesn't take into account the additional programming needed to read the ownership flags on all items already obtained.

This doesn't take into account RAM usage on the server end.