docs: Update examples to use stateless HTTP with JSON responses

[domdomegg]

Summary

Updates README and example code to consistently recommend and demonstrate stateless HTTP with JSON responses as the recommended pattern for production deployments.

Changes

• Update quickstart example to use stateless_http=True, json_response=True and make it executable
• Update all streamable HTTP mounting examples with recommended config
• Update OAuth server example with recommended config
• Reorder streamable_config.py to show recommended option first
• Change quickstart integration instructions to use Claude Code with HTTP transport
• Clarify that stateless HTTP + JSON is optimal for scalability

Rationale

This encourages users away from stdio/SSE/stateful HTTP patterns that have extra complexity and makes servers less reliable for most use cases. Stateless HTTP with JSON responses provides:

• Better scalability (no session state management)
• Simpler deployment (works across multiple instances)
• More reliability (simpler error recovery without SSE stream parsing)
• Lower complexity (no connection/session management overhead)

[felixweinberger]

It feels odd to me to go so all-in on stateless/json_response on every example when "stateless" on the MCP protocol spec doesn't even appear in a search yet.

I'm wondering if this causes potentially more confusion than help when the spec doesn't really provide a canonical description of how this is implemented?

Also I know @bhosmer-ant and @pja-ant are currently deep in discussions with the transport working group for what stateless looks like at the protocol layer, so I feel like going all in like this might be premature?

I think it'd be fine to increase the prominence of the stateless option (kind of like we do on TS? https://github.com/modelcontextprotocol/typescript-sdk?tab=readme-ov-file#without-session-management-recommended) but to make it look like the default seems a bit much?

[domdomegg]

Thanks! I've updated the PR to remove stateless_http=True from all the examples where it was newly added - see 8dbdfb2.

Also will note that the stateless_http implementation is already supported by the spec, see 2.5.1. "A server using the Streamable HTTP transport MAY assign a session ID at initialization time" - stateless_http in the Python SDK = just not doing this 'MAY' component. But can see there may be other transports changes soon anyways so won't push this further for now.