Fix UnboundLocalError in send_request when response not assigned

[maxisbey]

Fixes an intermittent UnboundLocalError that could occur in send_request() at the line checking isinstance(response_or_error, JSONRPCError).

Motivation and Context

We received a report of intermittent UnboundLocalError exceptions in send_request():

UnboundLocalError: cannot access local variable 'response_or_error' where it is not associated with a value

This can occur due to a race condition in anyio's fail_after context manager (anyio#589) where exceptions may be incorrectly suppressed, leaving the response_or_error variable unassigned while execution continues past the try/except block.

The fix:

• Initializes response_or_error to None before the try block
• Adds a _process_response static method with a defensive None check
• Handles EndOfStream and ClosedResourceError exceptions explicitly
• Uses try/except/else structure for cleaner control flow

How Has This Been Tested?

• Added unit tests for _process_response covering all code paths
• All existing session tests pass (23/23)
• Created a minimal reproduction script demonstrating the bug and fix

Breaking Changes

None. This is a defensive fix that handles edge cases more gracefully.

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

Closes #1717

The root cause is a race condition in anyio where fail_after's cancel scope can incorrectly suppress exceptions when a timeout and successful completion happen simultaneously. While this was reportedly fixed in anyio 4.0 (PR #591), edge cases may remain. This fix adds defensive code to handle the scenario gracefully rather than crashing with UnboundLocalError.