Integrate Phase 3 modules: storage swap, auth gating, route fixes

- Replace inline cache logic in api.py with api.storage abstraction
  (LocalStorage/GCSStorage), removing ~160 lines of dead code
- Wire waitlist and webhook routers into FastAPI app
- Add Clerk JWT auth (require_auth) to protected endpoints:
  POST /chat/completions/stream, POST/DELETE /api/wiki_cache,
  POST /api/wiki/regenerate_page
- Add WebSocket auth gating via query-param token on /ws/chat
- Fix sync/async bugs in route files (supabase_client methods are sync)
- Fix call signatures in webhooks.py (create_user, update_user)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: 2 people