feat(contrib/mcp-go): Record MCP Session ID as tag

[jboolean]

What does this PR do?

Records MCP session id as a tag on both tool and initialization spans.

Allows correlation of spans within a session.

Motivation

Relates to MLOB-4373

Reviewer's Checklist

• Changed code has unit tests for its functionality at or near 100% coverage.
• System-Tests covering this feature have been added and enabled with the va.b.c-dev version tag.
• There is a benchmark for any new code, or changes to existing code.
• If this interacts with the agent in a new way, a system test has been added.
• New code is free of linting errors. You can check this by running ./scripts/lint.sh locally.
• Add an appropriate team label so this PR gets put in the right place for the release notes.
• Non-trivial go.mod changes, e.g. adding new modules, are reviewed by @DataDog/dd-trace-go-guild.

Unsure? Have a question? Request a review!

[jboolean]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• feat(contrib/mcp-go): Record MCP Session ID as tag #4106 👈 (View in Graphite)
• feat(contrib/mcp-go): Trace MCP session initializations with MLObs spans #4101 : 2 other dependent PRs (#4115 , #4122 )
• feat(contrib/mcp-go): Initial mcp-go tracer implementation #4100
• main

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[pr-commenter]

Benchmarks

Benchmark execution time: 2025-11-14 15:38:34

Comparing candidate commit d9ed4ea in PR branch jb/contrib-mcp-go-session-tag with baseline commit 7f50759 in branch jb/contrib-mcp-go-init-span.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 9 metrics, 0 unstable metrics.

[datadog-datadog-prod-us1]

✅ Tests

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

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