One page for gifts, wherever they are actually sold.
About 5 mins
Guests want one link, not four shop accounts. Your registry page collects what you want from any shop, and a guest marks something as bought without having to say who they are — which is the only way a registry stays accurate.
Opening your registry link signed out shows your list, with nothing marked bought that has not been.
A gift bought twice? Claiming is anonymous on purpose — guests are far more likely to mark something taken when they are not being asked to sign in, and a registry nobody updates is the version that gets double-bought.