Fix stateless StreamableHttp connections

[cliffhall]

Description

When the client sends a request, do not pass on the mcp-session-id header for the Client <-> Proxy connection. This causes a problem for stateless http connections.

Motivation and Context

The changes in #787 introduced an unexpected side effect for stateless StreamableHttp connections. They don't return an mcp-session-id, but the function that forwards headers was passing on the mcp-session-id for the Client <-> Proxy transport. Therefore the server, which does not recognize this session id will return a 404 error according to spec.

Researching the headers being sent, it was that the Client <-> Proxy session id was being sent if no mcp-session-id was returned from the server.

This fixes #804

How Has This Been Tested?

With the server in #804 that was failing before. Works now.

Still works with Everything server, which gets it's proper session id sent on the Proxy <-> Server transport.

Breaking Changes

Nope.

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