Track migration to MCP spec 2026-07-28 (stateless model)

Nobody has claimed this yet.

## Summary

The MCP spec released a new revision on 2026-07-28 (announced at https://blog.modelcontextprotocol.io/posts/2026-07-28/) that moves from the stateful bidirectional protocol to a stateless request/response model — eliminating the `initialize`/`initialized` handshake and session IDs, replacing server-initiated elicitation with "Multi Round-Trip Requests" (MRTR), and deprecating Sampling, Roots, and Logging (12-month minimum deprecation window).

As of this issue, `@modelcontextprotocol/sdk` on npm is still on the `1.x` line (`1.30.0` latest) — no separate `2.0.0` package exists. The spec appears to be supported via 1.x releases.

## Why this is lower-priority here than in the other Mapbox MCP servers

Verified (`grep -rn "elicitInput\|createMessage" src/`): this repo uses **neither elicitation nor sampling** anywhere. Unlike `mcp-server` (mapbox/mcp-server#245) and `mcp-devkit-server` (mapbox/mcp-devkit-server#130), there's no elicitation-based or sampling-based UX here that the spec's deprecations would force a redesign of. The remaining relevant surface is just the stateless request/response transport model itself.

## What to check before starting

- [ ] Confirm real client support for the new stateless model (Claude Desktop, Claude Code, VS Code Copilot).
- [ ] Read the SDK's actual migration guide for the TypeScript SDK version(s) implementing 2026-07-28 support.
- [ ] Check whether anything in this server's transport/session handling assumes the old stateful handshake.

## Non-goals for now

- No urgency given the 12-month deprecation window.
- The routine SDK dependency bump (`1.29.0` → `1.30.0`) is handled separately and does not itself adopt the new spec — see the corresponding PR.

Start by inspecting the transport and session-handling code under src/ and confirm the current SDK version and migration guidance for the 2026-07-28 specification. Check real client support and whether the server assumes the stateful handshake; done means the required migration scope is identified and any necessary transport changes are completed or clearly documented.

Written by the indexing model from the issue text.