feat: propagate session_id from transport to tool context

[cbcoutinho]

Summary

This PR enables tools to access the transport-level session ID via Context.session_id, supporting session-level tracing and observability use cases.

Changes

• InitializationOptions: Add optional session_id field
• ServerSession: Store and expose session_id via property
• RequestContext: Add session_id field to dataclass
• StreamableHTTPSessionManager: Pass session_id when creating initialization options
• FastMCP Context: Add session_id property accessible in tools
• Tests: Comprehensive test suite for session_id propagation

Usage

Tools can now access the session ID like this:

@mcp.tool()
async def my_tool(ctx: Context) -> dict:
    session_id = ctx.session_id  # Transport's session ID (streamable-http)
    # Use for tracing, logging, correlation, etc.
    return {"session_id": session_id}

Behavior

• Streamable-HTTP (stateful): ctx.session_id returns the transport's session ID (UUID)
• Streamable-HTTP (stateless): ctx.session_id returns None (no session tracking)
• stdio/SSE transports: ctx.session_id returns None (session_id not set during initialization)

Use Cases

1. Distributed Tracing: Add session_id as a span attribute in OpenTelemetry traces to correlate all tool calls within a session
2. Session Analytics: Track per-session metrics and usage patterns
3. Debugging: Correlate logs and errors across multiple requests in the same session
4. Audit Trails: Associate all operations with a session identifier

Testing

• All 418 existing server tests pass ✓
• New test suite covers session_id propagation scenarios
• Verified no regressions in FastMCP, auth, resource tests

Fixes

• #485
• #942

Related

Related to #421 (OpenTelemetry tracing integration)

Breaking Changes

None. This is a backward-compatible addition:

• New optional field in InitializationOptions
• New property on Context (returns None if not available)
• Existing code continues to work without modifications