fix(internal/remoteconfig): allow Remote Config singleton to be reentrant

[darccio]

What does this PR do?

Models internal/remoteconfig package's behaviour to mirror how SetGlobalTracer behaves when calling Start() multiple times.

AI generated PR.

Motivation

Fixes #4111.

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!

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-11-20 11:39:02

Comparing candidate commit 9cf232b in PR branch dario.castane/langplat-901/duplicate-tracer-start-disables-rc with baseline commit a1926ab in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 18 metrics, 0 unstable metrics.

[felixge]

Gave this a light review, but mostly LGTM.

[datadog-datadog-prod-us1]

✅ Tests

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

_{This comment will be updated automatically if new data arrives.
🔗 Commit SHA: 9cf232b | Docs | Datadog PR Page | Was this helpful? Give us feedback!}

[darccio]

@codex review

[chatgpt-codex-connector]

💡 Codex Review

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[darccio]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Can't wait for the next one!

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[kakkoyun]

Looking good.

I believe we can simplify by using a mutex and regular boolean and just closing the client.stop once.

[kakkoyun]

We need to guard the Reset, I believe.

One other thing we can explore it to have an atomic.Pointer for the global client.

And embed the started logic into the Client since it has already have its own mutex. We can embed the logic in Start() into Client.start() and Start can proxy to it.

We can swap the global client after a successful start.
WDYT?

[darccio]

One other thing we can explore it to have an atomic.Pointer for the global client.

I tested this and it introduced too many changes. I think we need to find a better way to handle multiple products that run when the tracer is started.

[darccio]

/merge

[dd-devflow-routing-codex]

View all feedbacks in Devflow UI.

2025-11-20 15:51:25 UTC ℹ️ Start processing command /merge

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2025-11-20 15:51:30 UTC ℹ️ MergeQueue: pull request added to the queue

The expected merge time in main is approximately 45m (p90).

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2025-11-20 16:08:00 UTC ℹ️ MergeQueue: Readding this merge request to the queue because another merge request processed with yours failed. No action is needed from your side.

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2025-11-20 16:27:16 UTC ℹ️ MergeQueue: This merge request was merged