feat: initialize interactive live-stream game backend MVP

- Add FastAPI backend with WebSocket support
- Implement ConnectionManager for client connections
- Create GameEngine with async game loop (2s tick)
- Add RuleBasedAgent for keyword-based responses
- Define Pydantic schemas for GameEvent protocol
- Create debug frontend dashboard for testing

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/main.py

@@ -0,0 +1,102 @@
+"""
+FastAPI entry point for the interactive live-stream game backend.
+Configures the application, WebSocket routes, and lifecycle events.
+"""
+
+import logging
+from contextlib import asynccontextmanager
+
+from fastapi import FastAPI, WebSocket, WebSocketDisconnect
+from fastapi.middleware.cors import CORSMiddleware
+
+from .server import ConnectionManager
+from .engine import GameEngine
+from .schemas import GameEvent, ClientMessage, EventType
+
+# Configure logging
+logging.basicConfig(
+    level=logging.INFO,
+    format="%(asctime)s - %(name)s - %(levelname)s - %(message)s"
+)
+logger = logging.getLogger(__name__)
+
+# Global instances
+manager = ConnectionManager()
+engine = GameEngine(manager)
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    """
+    Application lifespan manager.
+    Starts the game engine on startup and stops it on shutdown.
+    """
+    logger.info("Starting application...")
+    await engine.start()
+    yield
+    logger.info("Shutting down application...")
+    await engine.stop()
+
+
+# Create FastAPI application
+app = FastAPI(
+    title="The Island - Live Stream Game Backend",
+    description="Commercial-grade interactive live-stream game backend",
+    version="0.1.0",
+    lifespan=lifespan
+)
+
+# Configure CORS for frontend access
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=["*"],
+    allow_credentials=True,
+    allow_methods=["*"],
+    allow_headers=["*"],
+)
+
+
+@app.get("/")
+async def root():
+    """Health check endpoint."""
+    return {
+        "status": "running",
+        "service": "The Island Game Backend",
+        "connections": manager.connection_count,
+        "engine_running": engine.is_running
+    }
+
+
+@app.websocket("/ws")
+async def websocket_endpoint(websocket: WebSocket):
+    """
+    WebSocket endpoint for real-time game communication.
+
+    Handles client connections and processes incoming messages.
+    """
+    await manager.connect(websocket)
+
+    # Send welcome message
+    welcome = GameEvent(
+        event_type=EventType.SYSTEM,
+        data={"message": "Connected to The Island!"}
+    )
+    await manager.send_personal(websocket, welcome)
+
+    try:
+        while True:
+            # Receive and parse client message
+            data = await websocket.receive_json()
+            message = ClientMessage(**data)
+
+            # Handle mock comment action
+            if message.action == "send_comment":
+                user = message.payload.get("user", "Anonymous")
+                text = message.payload.get("message", "")
+                await engine.process_comment(user, text)
+
+    except WebSocketDisconnect:
+        manager.disconnect(websocket)
+    except Exception as e:
+        logger.error(f"WebSocket error: {e}")
+        manager.disconnect(websocket)