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

Bắt đầu với việc xử lý shutdown của StreamableHTTPSessionManager và tái hiện sự cố bằng ví dụ streamable-http trên Python 3.12. Theo dõi cách các kết nối SSE hoặc streaming đang hoạt động bị hủy, sau đó xác minh rằng shutdown đóng chúng bằng một phản hồi HTTP phù hợp mà không xảy ra lỗi Uvicorn ASGI.