statistics: skip auto-analyze when it is executed outside the available time period (#49541)

[ti-chi-bot]

This is an automated cherry-pick of #49541

What problem does this PR solve?

Issue Number: close #49552

Problem Summary:

What changed and how does it work?

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]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: hawkingrei, winoros

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• OWNERS [hawkingrei,winoros]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-03-26 14:19:57.864360898 +0000 UTC m=+1991224.886607285: ☑️ agreed by hawkingrei.
• 2024-03-26 14:23:55.102838375 +0000 UTC m=+1991462.125084763: ☑️ agreed by winoros.

[codecov]

Codecov Report

❗ No coverage uploaded for pull request base (release-6.5@78dfdf2). Click here to learn what that means.
The diff coverage is 40.0000%.

Additional details and impacted files

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