Active Streamable HTTP sessions are not terminated during shutdown

Initial Checks

• I confirm that I'm using the latest version of MCP Python SDK
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Description

Context

This is primarily a repost of this fastmcp issue as it seems to actually be a bug in the mcp python sdk and I want to make sure we've got visibility over here.

When shutting down a FastMCP server (CTRL+C) while clients have active streaming connections, Uvicorn logs:

ERROR: ASGI callable returned without completing response.

The error occurs because StreamableHTTPSessionManager cancels the task group without first gracefully terminating active SSE/streaming connections.

Expected behavior would be the active connections being closed with a proper http response before the rest of shutdown.

Example Code

from fastmcp import FastMCP

mcp = FastMCP("Test Server")

@mcp.tool
def hello() -> str:
  return "Hello, World!"

if __name__ == "__main__":
  mcp.run(transport="streamable-http", port=8000)

Python & MCP Python SDK

Python 3.12
MCP Python SDK 1.26.0

StreamableHTTPSessionManager の shutdown 処理から始め、Python 3.12 で streamable-http の例を使って問題を再現します。アクティブな SSE 接続またはストリーミング接続がどのようにキャンセルされるかを追跡し、その後、shutdown によって適切な HTTP レスポンスとともに接続が閉じられ、Uvicorn ASGI エラーが発生しないことを確認します。