Closes #330

Motivation and Context

The load-balancing problem described in #330 has largely been addressed by stateless operation, the removal of sessions from the latest protocol lifecycle, and SessionStore-based restoration for legacy sessions. Stateless operation removes most cross-instance session routing, but it does not preserve an in-flight SSE response when the original connection or server instance disappears.

This PR closes that remaining gap with a shared EventStore. Event IDs are globally unique and identify their stream without a session ID, so another server instance can replay missed events from Last-Event-ID. Stateless handlers continue writing their response to the shared store after the original HTTP connection is dropped, and the client can reconnect without Mcp-Session-Id. Legacy session-based replay continues to use the same event-store contract.

How Has This Been Tested?

• Added a cross-instance legacy-session replay test.
• Added a stateless test that disconnects after a progress event, lets the original handler finish into the shared store, shuts down that instance, and replays the final response from another instance.
• Added client tests for sessionless reconnect and for refusing to reconnect before an event ID exists.
• Ran the Streamable HTTP disconnect, JSON response, priming, stale-session, event-store, unit, and doctest suites locally.

Breaking Changes

• StreamableHttpClient::get_stream and get_stream_with_max_sse_event_size now receive Option<Arc<str>> for the session ID. Custom HTTP client implementations must handle None for stateless replay.
• LocalSessionManager and NeverSessionManager no longer implement UnwindSafe or RefUnwindSafe because they contain an optional Arc<dyn EventStore>. Code that captures either manager across std::panic::catch_unwind must provide its own assertion or avoid that boundary.

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