docs(search): fix arrow keys skipping multiple items

Refactor useSearch to true singleton pattern. Previously, each component
calling useSearch() registered its own useToggleScope hotkeys, causing
~7 handlers to fire per keypress.

- Move computeds, watchers, and useToggleScope to module level
- Simplify useSearch() to just return singleton interface
- Hotkeys now register exactly once when module loads

Author: johnleider