feat: wire chat UI to backend APIs

- Created API clients for LLM chat (/api/llm/chat) and Ideas (/api/ideas)
- Implemented useChat hook for conversation state management
- Connected Chat component to backend with full CRUD operations
- Integrated ConversationSidebar with conversation fetching
- Added automatic conversation persistence after each message
- Integrated WebSocket for connection status
- Used existing better-auth for authentication
- All TypeScript strict mode compliant (no any types)

Deliverables:
✅ Working chat interface at /chat route
✅ Conversations save to database via Ideas API
✅ Real-time WebSocket connection
✅ Clean TypeScript (no errors)
✅ Full conversation loading and persistence

See CHAT_INTEGRATION_SUMMARY.md for detailed documentation.

apps/web/src/lib/api/index.ts

@@ -0,0 +1,14 @@
+/**
+ * API Client Exports
+ * Central export point for all API client modules
+ */
+
+export * from "./client";
+export * from "./chat";
+export * from "./ideas";
+export * from "./tasks";
+export * from "./events";
+export * from "./knowledge";
+export * from "./domains";
+export * from "./teams";
+export * from "./personalities";