server: fix incorrect setting of health status (#51595)

[ti-chi-bot]

This is an automated cherry-pick of #51595

What problem does this PR solve?

Issue Number: close #51596

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.

Fix that when the server is not started, it should not default to a healthy state

[ti-chi-bot]

@hawkingrei: Your lgtm message is repeated, so it is ignored.

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[codecov]

Codecov Report

❗ No coverage uploaded for pull request base (release-6.5@9220d94). Click here to learn what that means.
The diff coverage is 100.0000%.

Additional details and impacted files

@@               Coverage Diff                @@
##             release-6.5     #51632   +/-   ##
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  Lines                  ?     350919           
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  Hits                   ?     258401           
  Misses                 ?      75905           
  Partials               ?      16613           

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

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

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-03-27 03:15:55.327871698 +0000 UTC m=+2037782.350118084: ☑️ agreed by hawkingrei.
• 2024-03-27 06:26:58.219455799 +0000 UTC m=+2049245.241702186: ☑️ agreed by AilinKid.