Is your feature request related to a problem? Please describe.

I would like to see Opentelemetry traces and Metrics baked into SDK.
E.g.

1. Traces emitted on all Requests from client and server side of MCP SDK.
2. Metrics for tool/prompt/resource calls

Describe the solution you'd like

I am trying to use Opentelemetry sdk to add traces and metrics features.

Steps

1. Creating session in client and server.
2. Initialise tracer (Opentelemetry tracer instances) in BaseSession (src/mcp/shared/session.py).
3. Binding trace context (traceparent) to _meta of RequestParams.Meta before sending request from client (send_request in src/mcp/shared/session.py)
4. In server use the traceparent from received request to create new span with incoming span as parent span.

Describe alternatives you've considered

I tried to implement the same via traceloop. I was not able to get correct parent - child relationship between spans while doing so.

Additional context

I am able to achieve distributed tracing across my Agentic application and MCP server.