#706 Fix back navigation from post to hivesense search

Problem: After clicking a search result and pressing back,
users saw an empty page instead of search results.

Fix:
- ai-result.tsx: Use useMemo for displayedPosts derived from
  React Query cache (fullPosts) + loaded stubs. This ensures
  data persists on back navigation.
- use-search.ts: Add useEffect to sync input state with URL
  params when navigating back.

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>