feat(web): chat UI with conversations, messages, and WebSocket streaming

Build the primary chat interface with conversation list sidebar,
message display area, streaming assistant responses via socket.io,
and auto-scrolling. Supports creating new conversations, sending
messages with optimistic updates, and real-time text streaming
from the agent via WebSocket events.

Components: ConversationList, MessageBubble, ChatInput, StreamingMessage
Libs: socket.io client singleton, shared types for Conversation/Message

Refs #28

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

apps/web/package.json

@@ -17,6 +17,7 @@
     "next": "^16.0.0",
     "react": "^19.0.0",
     "react-dom": "^19.0.0",
+    "socket.io-client": "^4.8.0",
     "tailwind-merge": "^3.5.0"
   },
   "devDependencies": {