ClosedResourceError During MCP Stateless Server Shutdown When Sending Log Messages

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

I'm seeing occasional errors from our MCP server, which I think are a race condition during shutdown.

I think this is a similar but distinct issue to the race condition in #1190 and #1384 as this is during send_log_message

I haven't been able to get a consistent reproduce yet, will update when I can.

Stack Trace

+ Exception Group Traceback (most recent call last):
  |   File "/app/.venv/lib/python3.13/site-packages/mcp/server/streamable_http_manager.py", line 180, in run_stateless_server
  |     await self.app.run(
  |     ...<4 lines>...
  |     )
  |   File "/app/.venv/lib/python3.13/site-packages/fastmcp/server/low_level.py", line 202, in run
  |     async with AsyncExitStack() as stack:
  |                ~~~~~~~~~~~~~~^^
  |   File "/usr/local/lib/python3.13/contextlib.py", line 768, in __aexit__
  |     raise exc
  |   File "/usr/local/lib/python3.13/contextlib.py", line 751, in __aexit__
  |     cb_suppress = await cb(*exc_details)
  |                   ^^^^^^^^^^^^^^^^^^^^^^
  |   File "/app/.venv/lib/python3.13/site-packages/mcp/shared/session.py", line 238, in __aexit__
  |     return await self._task_group.__aexit__(exc_type, exc_val, exc_tb)
  |            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  |   File "/app/.venv/lib/python3.13/site-packages/anyio/_backends/_asyncio.py", line 783, in __aexit__
  |     raise BaseExceptionGroup(
  |         "unhandled errors in a TaskGroup", self._exceptions
  |     ) from None
  | ExceptionGroup: unhandled errors in a TaskGroup (1 sub-exception)
  +-+---------------- 1 ----------------
    | Exception Group Traceback (most recent call last):
    |   File "/app/.venv/lib/python3.13/site-packages/fastmcp/server/low_level.py", line 214, in run
    |     async with anyio.create_task_group() as tg:
    |                ~~~~~~~~~~~~~~~~~~~~~~~^^
    |   File "/app/.venv/lib/python3.13/site-packages/anyio/_backends/_asyncio.py", line 783, in __aexit__
    |     raise BaseExceptionGroup(
    |         "unhandled errors in a TaskGroup", self._exceptions
    |     ) from None
    | ExceptionGroup: unhandled errors in a TaskGroup (1 sub-exception)
    +-+---------------- 1 ----------------
      | Traceback (most recent call last):
      |   File "/app/.venv/lib/python3.13/site-packages/mcp/server/lowlevel/server.py", line 694, in _handle_message
      |     await session.send_log_message(
      |     ...<3 lines>...
      |     )
      |   File "/app/.venv/lib/python3.13/site-packages/mcp/server/session.py", line 213, in send_log_message
      |     await self.send_notification(
      |     ...<10 lines>...
      |     )
      |   File "/app/.venv/lib/python3.13/site-packages/mcp/shared/session.py", line 335, in send_notification
      |     await self._write_stream.send(session_message)
      |   File "/app/.venv/lib/python3.13/site-packages/anyio/streams/memory.py", line 249, in send
      |     self.send_nowait(item)
      |     ~~~~~~~~~~~~~~~~^^^^^^
      |   File "/app/.venv/lib/python3.13/site-packages/anyio/streams/memory.py", line 218, in send_nowait
      |     raise ClosedResourceError
      | anyio.ClosedResourceError
      +------------------------------------

Python & MCP Python SDK

MCP SDK Version: 1.25.0
via fastmcp Version: 2.14.4
Python Version: 3.13.5