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/server.py

@@ -0,0 +1,90 @@
+"""
+WebSocket connection manager and server utilities.
+Handles client connections, disconnections, and message broadcasting.
+"""
+
+import logging
+from typing import Any
+from fastapi import WebSocket
+
+from .schemas import GameEvent
+
+logger = logging.getLogger(__name__)
+
+
+class ConnectionManager:
+    """
+    Manages WebSocket connections for real-time communication.
+
+    Handles connection lifecycle and provides broadcast capabilities
+    to all connected clients.
+    """
+
+    def __init__(self) -> None:
+        """Initialize the connection manager with an empty connection list."""
+        self._active_connections: list[WebSocket] = []
+
+    @property
+    def connection_count(self) -> int:
+        """Return the number of active connections."""
+        return len(self._active_connections)
+
+    async def connect(self, websocket: WebSocket) -> None:
+        """
+        Accept and register a new WebSocket connection.
+
+        Args:
+            websocket: The WebSocket connection to accept
+        """
+        await websocket.accept()
+        self._active_connections.append(websocket)
+        logger.info(f"Client connected. Total connections: {self.connection_count}")
+
+    def disconnect(self, websocket: WebSocket) -> None:
+        """
+        Remove a WebSocket connection from the active list.
+
+        Args:
+            websocket: The WebSocket connection to remove
+        """
+        if websocket in self._active_connections:
+            self._active_connections.remove(websocket)
+            logger.info(f"Client disconnected. Total connections: {self.connection_count}")
+
+    async def broadcast(self, event: GameEvent) -> None:
+        """
+        Send a GameEvent to all connected clients.
+
+        Args:
+            event: The GameEvent to broadcast
+        """
+        if not self._active_connections:
+            return
+
+        message = event.model_dump_json()
+        disconnected: list[WebSocket] = []
+
+        for connection in self._active_connections:
+            try:
+                await connection.send_text(message)
+            except Exception as e:
+                logger.warning(f"Failed to send to client: {e}")
+                disconnected.append(connection)
+
+        # Clean up failed connections
+        for conn in disconnected:
+            self.disconnect(conn)
+
+    async def send_personal(self, websocket: WebSocket, event: GameEvent) -> None:
+        """
+        Send a GameEvent to a specific client.
+
+        Args:
+            websocket: The target WebSocket connection
+            event: The GameEvent to send
+        """
+        try:
+            await websocket.send_text(event.model_dump_json())
+        except Exception as e:
+            logger.warning(f"Failed to send personal message: {e}")
+            self.disconnect(websocket)