All search state serialized into URL query parameters for back/forward navigation

When search state lives only in client memory, the back button becomes useless, sharing a result page over Slack or email delivers the unfiltered homepage, and refreshing the tab wipes every refinement. Users expect URLs to be durable addresses — breaking that contract means every deep link from Google, Reddit, or a friend lands on the wrong state. URL-synced state is also the only reliable way to give users back/forward history through their filter exploration, which doubles as an undo stack.

Drive all filter, sort, and pagination state through URLSearchParams and router.push. Read initial values from useSearchParams on mount so the URL is the single source of truth. Edit app/listings/search/page.tsx:

const updateFilters = (next) => {
  const params = new URLSearchParams(searchParams)
  Object.entries(next).forEach(([k, v]) => v ? params.set(k, v) : params.delete(k))
  router.push(`?${params}`)
}