Part of #421

Depends on

• OpenTelemetry inject trace context propagation in _meta #2093
• Propagate contextvars through anyio streams #1996
• OpenTelemetry extract trace context from _meta in incoming requests #2133

Motivation and Context

Implements the minimal client side tracing portion as specified in https://github.com/open-telemetry/semantic-conventions/blob/v1.40.0/docs/gen-ai/mcp.md#client

• This only includes the "required" attributes for now.
• I threaded a new TracerProvider optional parameter into the MCP client and server sessions for DI purposes. That way users and test code can isolate the span creation.
• This also covers calls from server -> client like sampling and notifications.

How Has This Been Tested?

Added lots of new test cases showing spans and their parent child relationships.

Breaking Changes

No

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

Additional context