Fix unhandled TaskGroup exceptions that occur in transport layer

[Kulaxyz]

Fixing unhandled TaskGroup exceptions that occur in transport layer

Motivation and Context

When MCP server is down or HTTP errors occur (5xx), TaskGroup exceptions are not being properly converted to error responses for pending requests. The response stream never receives the error, causing clients that are waiting for stream responses to hang indefinitely.

This affects any client implementation that waits synchronously for responses from the transport layer, as they never receive the error notifications needed to handle failures gracefully.

How Has This Been Tested?

• Verified that TaskGroup exceptions are properly forwarded to read streams
• Confirmed error responses are delivered immediately with correct JSON-RPC format
• All existing transport tests continue to pass

Breaking Changes

No

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

Strands SDK is an example of an implementation that is hanging when MCP Server is down.