fix: handle_sse_response causing dangling client's read_stream

[ivanbelenky]

Notifying session layer on transport error. Sending the error to the client's read_stream_writer.

Motivation and Context

Indefinitely hang described on issue #1811

How Has This Been Tested?

Running suite of tests locally as per contribution guidelines.

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

[heyhayes]

Hey @ivanbelenky — thanks for identifying this root cause, your analysis was spot on. PR #2122 covers the same fix (sending a JSONRPCError when the SSE stream ends without a response) and also addresses the infinite reconnection loop in _handle_reconnection and handle_get_stream that was reported in #1789. Just wanted to flag the overlap so we don't duplicate effort.