Add pluggable instrumentation interface and request_id logging

[dgenio]

Summary

This PR introduces a pluggable instrumentation interface with a token-based API for the MCP Python SDK, enabling OpenTelemetry and other observability integrations as requested in #421.

Key Innovation: Token-Based API

The instrumentation interface uses a token-based approach that solves a critical design problem:

class Instrumenter(Protocol):
    def on_request_start(...) -> Any:  # Returns a token
        """Start instrumentation, return state token (e.g., OTel span)"""
    
    def on_request_end(token: Any, ...) -> None:  # Receives the token
        """End instrumentation using the token"""
    
    def on_error(token: Any, ...) -> None:  # Receives the token
        """Handle errors using the token"""

This design enables instrumenters to maintain state (like OpenTelemetry spans) without external storage or side-channels, addressing feedback from the community on API design best practices.

Changes

Core Interface

• Defined Instrumenter protocol with token-based hooks
• Created NoOpInstrumenter as default implementation with minimal overhead
• Token can be any value (span object, dict, etc.)

Integration

• Added instrumenter parameter to ServerSession and ClientSession constructors
• Wired instrumentation into Server._handle_request() to track:
  • Request start/end with duration tracking
  • Success/failure status
  • Error occurrences with token propagation
• Added request_id to logging extra fields for correlation

OpenTelemetry Example

• NEW: Complete OpenTelemetryInstrumenter implementation in examples/opentelemetry_instrumentation.py
• Demonstrates span management using tokens
• Includes setup code and runnable example
• Shows proper error recording and status codes

Testing

• Comprehensive tests verifying:
  • Token flow from start → end/error
  • Hooks are invoked for successful and failed requests
  • request_id is consistent across lifecycle
  • Metadata is passed correctly
  • Default no-op behavior works

Documentation

• Added docs/instrumentation.md with:
  • Token-based API explanation with "Why Tokens?" section
  • Complete OpenTelemetry integration guide
  • Usage examples for server and client
  • Custom metrics example
  • Best practices and migration guide

Benefits

1. No External Storage: Instrumenters don't need spans = {} dictionaries
2. OpenTelemetry Compatible: Spans can be returned and passed directly
3. Thread-Safe: Each request gets its own token
4. Automatic Cleanup: Tokens are garbage collected
5. Flexible: Token can be any value

Follow-up Work

• Package OpenTelemetry instrumenter as installable extra (pip install mcp[opentelemetry])
• Additional built-in instrumenters (Prometheus, StatsD, Datadog)
• Distributed tracing via params._meta.traceparent propagation
• Client-side instrumentation (server-side is complete)

Fixes #421

[dgenio]

Updated the instrumentation interface to use a token-based API based on community feedback. This enables proper OpenTelemetry integration without external storage. See updated PR description for details.