fix: add diagnostics to client and track autocapture getHierachy block time

[Mercy811]

Summary

• Diagnostics client
  • Implement sample rate logic
    • Rename isSessionInSample() to isTimestampInSample() and move it from SR to core package
  • Save current timestamp as last flush timestamp for first time users. Otherwise events are not sent when a first time user comes back next time because it still thinks this user is first time user.
• Add diagnostics client to browser client
• Add a backdoor to set diagnostics sample rate. Call it before amplitude.init().
• Use diagnostics client to
  • track analytics sdk library + version
  • track autocapture getHierachy block time
• Use remote config in autocapture plugin
• Gitignore playground amplitude.js script

Ideally, both remote config client and diagnostics client should be in AmplitudeContext but it requires significant change so this PR adds them to internal browser config.

Checklist

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Note

Introduces a diagnostics client with sampling, integrates it into the browser/unified clients, tracks autocapture getHierarchy timing, and switches autocapture to use a provided remote-config client.

• Core:
  • Add DiagnosticsClient (tags/counters/histograms/events, flush/save timers) with deterministic sampling (generateHashCode, isTimestampInSample).
  • Export diagnostics and sampling utilities; update types (AmplitudeContext -> interfaces) and configs to carry diagnosticsClient/remoteConfigClient.
• Browser/Unified Clients:
  • Initialize and attach DiagnosticsClient; set library tag; expose _setDiagnosticsSampleRate backdoor; plumb through config (enableDiagnostics, diagnosticsSampleRate).
  • Pass remoteConfigClient through; factories wrap new method.
• Autocapture Plugin:
  • Track getHierarchy duration via diagnostics histogram.
  • Replace internal RC fetch with provided remoteConfigClient.subscribe.
• Session Replay:
  • Reuse core isTimestampInSample (remove local sampler).
• Housekeeping/Tests:
  • Add tests for diagnostics, sampling, and new APIs; ignore playground amplitude.js in .gitignore.

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[Mercy811]

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[daniel-graham-amplitude]

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[cursor]

✅ Bugbot reviewed your changes and found no bugs!

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[daniel-graham-amplitude]

Lgtm. Some minor comments.

I'll definitely want SR and Autocapture reviewers to approve this first though.

[lewgordon-amplitude]

SR changes (sampling changes) LGTM!