feat(metrics): [Trace Metrics 22] Close and flush MetricsBatchProcessor from SentryClient

[adinauer]

📜 Description

💡 Motivation and Context

💚 How did you test it?

📝 Checklist

• I added GH Issue ID & Linear ID
• I added tests to verify the changes.
• No new PII added or SDK only sends newly added PII if sendDefaultPII is enabled.
• I updated the docs if needed.
• I updated the wizard if needed.
• Review from the native team if needed.
• No breaking change or entry added to the changelog.
• No breaking change for hybrid SDKs or communicated to hybrid SDKs.

🔮 Next steps

[github-actions]

	Fails
🚫	Please consider adding a changelog entry for the next release.

	Messages
📖	Do not forget to update Sentry-docs with your feature once the pull request gets approved.

Instructions and example for changelog

Please add an entry to CHANGELOG.md to the "Unreleased" section. Make sure the entry includes this PR's number.

Example:

## Unreleased

### Features

- [Trace Metrics 22] Close and flush `MetricsBatchProcessor` from `SentryClient` ([#5010](https://github.com/getsentry/sentry-java/pull/5010))

If none of the above apply, you can opt out of this check by adding #skip-changelog to the PR description or adding a skip-changelog label.

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[adinauer]

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• feat(metrics): [Trace Metrics 23] Add E2E tests for Metrics #5011
• feat(metrics): [Trace Metrics 22] Close and flush MetricsBatchProcessor from SentryClient #5010 👈 (View in Graphite)
• Use uv for managing python version #5009
• feat(metrics): [Trace Metrics 21] Add AI rules files for Metrics (and update feature flags rule) #5008
• feat(metrics): [Trace Metrics 20] Add device and OS attributes to metrics #5007
• feat(metrics): [Trace Metrics 19] Create SentryMetricsParameters for Metrics #5006
• feat(metrics): [Trace Metrics 18] Add unit tests for Metrics #5005
• feat(metrics): [Trace Metrics 17] Remove Experimental Annotation from Metrics Options #4996
• feat(metrics): [Trace Metrics 16] Only send user attributes if sendDefaultPii is true #4995
• feat(metrics): [Trace Metrics 15] Android Metrics batch processor and factory #4994
• feat(metrics): [Trace Metrics 14] Metrics Manifest options for Android #4993
• feat(metrics): [Trace Metrics 13] Metrics external options #4992
• feat(metrics): [Trace Metrics 12] Record client report for discarded metrics envelope item #4991
• feat(metrics): [Trace Metrics 11] Metrics Envelope item deserialization #4990
• feat(metrics): [Trace Metrics 10] Metrics Gauge API #4989
• feat(metrics): [Trace Metrics 9] Metrics Distribution API #4988
• feat(metrics): [Trace Metrics 8] Metrics Count API #4987
• feat(metrics): [Trace Metrics 7] Metrics counter basic API #4986
• feat(metrics): [Trace Metrics 6] Implement SentryClient for Metrics #4985
• feat(metrics): [Trace Metrics 5] Add batch processor for Metrics #4984
• feat(metrics): [Trace Metrics 4] Add transport types for metrics #4983
• feat(metrics): [Trace Metrics 3] Enable metrics by default #4982
• feat(metrics): [Trace Metrics 2] MetricsApi stub #4981
• feat(metrics): [Trace Metrics 1] Metrics Options #4980
• main

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