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>

run.py

@@ -0,0 +1,16 @@
+#!/usr/bin/env python3
+"""
+Startup script for The Island game backend.
+Runs the FastAPI server with uvicorn and hot-reloading enabled.
+"""
+
+import uvicorn
+
+if __name__ == "__main__":
+    uvicorn.run(
+        "backend.app.main:app",
+        host="0.0.0.0",
+        port=8000,
+        reload=True,
+        log_level="info"
+    )