docs(examples): add minimal remote MCP server example

[travisbreaks]

Summary

Adds a focused, well-documented example of a remote MCP server using StreamableHTTP transport. This addresses the documentation gap described in #777.

The existing simpleStreamableHttp.ts example includes OAuth, tasks, elicitation, and other advanced features that make it hard for newcomers to identify the minimal setup. The new remoteServer.ts example strips away everything except what you need to get a working remote server:

• Session management: tracks connected clients via Mcp-Session-Id header
• Streaming responses: tools that emit progress notifications via SSE
• Tools, resources, and prompts: one of each, clearly commented
• Graceful shutdown: closes all active transports on SIGINT
• Claude Desktop config: shows the exact JSON to connect

The example is ~200 lines, fully commented, and runnable with a single command:

pnpm --filter @modelcontextprotocol/examples-server exec tsx src/remoteServer.ts

Test plan

• pnpm build:all passes
• pnpm --filter @modelcontextprotocol/examples-server run lint passes
• Server starts and accepts connections from MCP Inspector
• greet tool returns expected response
• count tool streams log notifications during execution
• server-info resource returns JSON with uptime
• summarize prompt returns expected template
• Session termination via DELETE works correctly

Fixes #777

🤖 Generated with Claude Code

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