feat(server): implement websocket chat backend

app/main.py

@@ -0,0 +1,36 @@
+from pathlib import Path
+
+from fastapi import FastAPI
+from fastapi.responses import FileResponse
+from fastapi.staticfiles import StaticFiles
+
+from app.websocket.chat import router as chat_router
+from app.websocket.manager import manager
+
+BASE_DIR = Path(__file__).resolve().parent
+STATIC_DIR = BASE_DIR / "static"
+
+app = FastAPI(title="Simple WebSocket Chatroom")
+
+# WebSocket route: ws://localhost:8000/ws/{room_id}/{client_id}
+app.include_router(chat_router)
+
+# Frontend files
+app.mount("/static", StaticFiles(directory=STATIC_DIR), name="static")
+
+
+@app.get("/")
+async def home():
+    """Serve the chatroom GUI."""
+    return FileResponse(STATIC_DIR / "index.html")
+
+
+@app.get("/api/rooms")
+async def rooms():
+    """Small helper endpoint for the GUI/debugging."""
+    return manager.rooms_overview()
+
+
+@app.get("/health")
+async def health():
+    return {"status": "ok", "app": "Simple WebSocket Chatroom"}