Add SSEEdgeTransport

[imownbey]

Adds a transport which can be used in environments like Vercel and Cloudflare Workers. I called this SSEEdgeTransport but imagine there is some better naming.

I also added documentation to the readme on how to use it (with Hono which is a popular web framework for Cloudflare) and a section on using it with Cloudflare Durable Objects to keep track of different servers.

Motivation and Context

The current documentation & transport only really work with Node or Express which is pretty limiting in my experience. I think Durable Objects offer a viable quick way to get something spun up, and regardless a Transport which works in Edge environments is useful.

How Has This Been Tested?

Ran locally, deployed to cloudflare and tested with Cursor and a basic MCP Server (the greeting one).

I didn't test disconnects too much because I am not super familiar with MCP's reconnection protocol. But assuming the client keeps sending the same SessionID it will get directed to the same Durable Object (as described in the README, this is independent of the actual code change).

Breaking Changes

None

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