fix(stdio): resolve BrokenResourceError race condition on quick exit

[gspeter-max]

ROOT CAUSE:
The stdio_client async context manager had a race condition when exiting quickly (before subprocess finished outputting data). The cleanup code in the finally block closed memory streams while background tasks (stdout_reader and stdin_writer) were still using them, resulting in BrokenResourceError.

Timeline of the bug:

1. User code exits the async with stdio_client(...) context
2. The finally block executes
3. Streams are closed immediately
4. Background tasks are still running and trying to send/receive data
5. Tasks encounter closed streams → BrokenResourceError

CHANGES:

1. Added BrokenResourceError to exception handlers in both client and server

   • src/mcp/client/stdio.py: Lines 161, 177 (stdout_reader, stdin_writer)
   • src/mcp/server/stdio.py: Lines 67, 77 (stdin_reader, stdout_writer)
   • This allows tasks to exit gracefully if streams close during operation

2. Added task cancellation before stream closure in client transport

   • src/mcp/client/stdio.py: Line 210 (after process cleanup)
   • tg.cancel_scope.cancel() sends cancellation signal to background tasks
   • Tasks receive signal and finish their current operation
   • Then streams are closed (tasks aren't using them anymore)

3. Added regression test

   • tests/client/test_stdio.py: test_stdio_client_quick_exit_race_condition
   • Verifies that quick context exits don't cause ExceptionGroup crashes

IMPACT:

• No more ExceptionGroup crashes when exiting quickly
• Graceful task shutdown with proper cancellation
• Backward compatible - all existing tests pass
• Better resource cleanup - tasks finish before streams close

TECHNICAL NOTES:

• Server transport only needed exception handler changes (not task cancellation) because it doesn't manage subprocess lifecycle
• The fix uses defense-in-depth: both proper coordination AND graceful handling
• anyio.BrokenResourceError is raised when operations are attempted on closed resources, distinct from ClosedResourceError (resource already closed)

FILES MODIFIED:

• src/mcp/client/stdio.py
• src/mcp/server/stdio.py
• tests/client/test_stdio.py

Motivation and Context

How Has This Been Tested?

Breaking Changes

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context