Render the search icon immediately

[walishcs]

What changed

• Change the SearchPalette island from client-only rendering to server rendering with client-load hydration.
• Keep the existing Astryx IconButton, SVG, Pagefind preload, and command palette behavior unchanged.

Why

The client-only island emitted no search button in the initial HTML, so the icon appeared only after React loaded. Server rendering places the icon in the first response while React attaches its interactions during page load.

Validation

• npm run check
• npm test (25 tests)
• npm run format:check
• npm run build
• npm run astryx -- doctor
• Confirmed the search icon is visible at DOMContentLoaded and opens the hydrated command palette.