Scalable Product Filtering and Search Persistence using Zustand

Act as a Technical SEO and UX Developer. Architect a highly scalable Zustand store dedicated entirely to e-commerce product search and faceted filtering. The state must cleanly ingest and manage a massive [FILTER_SCHEMA] including dynamic categories, min/max price ranges, and boolean attributes. You must implement a flawless [URL_QUERY_SYNC] mechanism (utilizing `history.pushState` or Next.js router) ensuring that every single mutation in the Zustand filter state instantly serializes and updates the browser URL, rendering the exact search configuration bookmarkable and SEO-crawlable. Inject a strict [DEBOUNCE_TIME] (e.g., 300ms) into the search string action to prevent spamming the backend API. Focus heavily on intercepting the native browser 'Back/Forward' popstate events to inversely update the Zustand store from the URL.