syncer: exit watch leader immediately (#8824)

[ti-chi-bot]

This is an automated cherry-pick of #8824

What problem does this PR solve?

Issue Number: Close #8823

What is changed and how does it work?

Check List

Tests

• Unit test

Release note

None.

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Please upload report for BASE (release-8.5@fb992f9). Learn more about missing BASE report.

Additional details and impacted files

@@              Coverage Diff               @@
##             release-8.5    #8831   +/-   ##
==============================================
  Coverage               ?   75.58%           
==============================================
  Files                  ?      461           
  Lines                  ?    72295           
  Branches               ?        0           
==============================================
  Hits                   ?    54641           
  Misses                 ?    14154           
  Partials               ?     3500           

Flag	Coverage Δ
unittests	75.58% <100.00%> (?)

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---- 🚨 Try these New Features:

• Flaky Tests Detection - Detect and resolve failed and flaky tests

[ti-chi-bot]

This cherry pick PR is for a release branch and has not yet been approved by triage owners.
Adding the do-not-merge/cherry-pick-not-approved label.

To merge this cherry pick:

1. It must be approved by the approvers firstly.
2. AFTER it has been approved by approvers, please wait for the cherry-pick merging approval from triage owners.

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