How to use async graph with the add_fastapi_endpoint method?

[About-Gleaning]

I'm a beginner Python developer working on a project using FastAPI and LangGraph. I encountered an issue while integrating ag-ui:
My graph uses MCP tools, which makes my graph asyn
How can I use an async graph with the add_fastapi_endpoint method?

Here's part of my code - is my solution correct?"

async def get_graph():
    client = MultiServerMCPClient({
        "mcp-server": {
            "url": "http://127.0.0.1:8080/sse",
            "transport": "sse"
        }
    })
    mcp_tools = await client.get_tools()
    ...
    graph_builder = StateGraph(SupplierState)
   ...
    graph = graph_builder.compile(name="demo-graph", checkpointer=checkpointer)
  
    return graph

main.py

app = FastAPI()

@app.on_event("startup")
async def startup_event():
    graph = await get_graph()
    sdk = CopilotKitRemoteEndpoint(
        agents=[
            LangGraphAgent(
                name="demo-graph",
                description="my graph",
                graph=graph
            ),
        ],
    )
    add_fastapi_endpoint(app, sdk, "/copilotkit", use_thread_pool=False)

What is the correct way to register an async graph as a FastAPI endpoint?"