statistics: add recover to protect background task (#58739)

[ti-chi-bot]

This is an automated cherry-pick of #58739

What problem does this PR solve?

Issue Number: close #58738

ref #58715

Problem Summary:

What changed and how does it work?

#58715 bug will panic in the background. it will make this background exiting and cannot restart it. it will lead many critical bug. so we need to add recover to protect the background thread.

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No need to test

  • I checked and no code files have been changed.

Side effects

• Performance regression: Consumes more CPU
• Performance regression: Consumes more Memory
• Breaking backward compatibility

Documentation

• Affects user behaviors
• Contains syntax changes
• Contains variable changes
• Contains experimental features
• Changes MySQL compatibility

Release note

Please refer to Release Notes Language Style Guide to write a quality release note.

None

[ti-chi-bot]

@ti-chi-bot: The following tests failed, say /retest to rerun all failed tests or /retest-required to rerun all mandatory failed tests:

Test name	Commit	Details	Required	Rerun command
idc-jenkins-ci-tidb/build	964ef56	link	true	/test build
idc-jenkins-ci-tidb/check_dev	964ef56	link	true	/test check-dev
idc-jenkins-ci-tidb/unit-test	964ef56	link	true	/test unit-test

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[fixdb]

+1

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2025-09-23 01:55:26.695699779 +0000 UTC m=+321736.766193462: ☑️ agreed by fixdb.