Improve Pagefind search responsiveness

[walishcs]

What changed

• Preload the Pagefind runtime when search receives focus, hover, or opens.
• Use Pagefind debounced search with a fixed 200 ms timeout.
• Limit initial result hydration to six entries and cache query-specific result data.
• Ignore superseded queries and preserve the existing Astryx CommandPalette behavior.
• Add focused unit coverage for preparation, debounce, limits, caching, and stale searches.

Why

The first query previously paid the runtime initialization cost, every keystroke could start work, and up to twelve result payloads were loaded before rendering. This made search feel delayed and scales poorly as the index grows.

Validation

• npm run check
• npm test (25 tests)
• npm run format:check
• npm run build (17 Pagefind pages indexed)
• npm run astryx -- doctor
• Production browser smoke test: results rendered in about 227 ms after warm-up, rapid input kept only the latest query, and keyboard controls remained functional.