Revert Kapa-powered search chat integration

[Copilot]

This PR backs out commit 689ed2a15f76b82ac0f759c66ff12ce0966cf2a0, which introduced the Kapa-based search chat flow. It restores the prior search UX and removes the Kapa integration surface from the app.

• Search UX rollback

  • Restores the previous SearchModal, SearchButton, and SearchContext behavior/state model.
  • Removes Kapa-driven chat/search interactions added in the reverted commit.

• App wiring cleanup

  • Removes Kapa-specific root-route wiring and related integration hooks.
  • Reverts environment/config touchpoints introduced for the chat integration.

• Dependency surface rollback

  • Removes Kapa-related package additions and corresponding lockfile changes.

// __root.tsx (conceptual)
- import { KapaSearchProvider } from '@/...'
- <KapaSearchProvider><App /></KapaSearchProvider>
+ <App />