On a product listing page, users want to share a link that reproduces their current filters, sort order and page. Where should that state live?

Filters, sort order and page belong in the URL query string. URL state survives a reload, works with the back and forward buttons, and can be shared as a link. That is exactly what these need. "In a global client store such as Redux" is the tempting wrong answer. A global store, like React context, loses the state on reload and cannot be shared by link.