[release-20.0] Fix vttablet not being marked as not serving when MySQL stalls (#17883)

[vitess-bot]

Description

This is a backport of #17883

[vitess-bot]

Review Checklist

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General

• Ensure that the Pull Request has a descriptive title.
• Ensure there is a link to an issue (except for internal cleanup and flaky test fixes), new features should have an RFC that documents use cases and test cases.

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Backward compatibility

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• vtctl command output order should be stable and awk-able.

[codecov]

Codecov Report

Attention: Patch coverage is 66.66667% with 2 lines in your changes missing coverage. Please review.

Project coverage is 66.42%. Comparing base (a4a6ed3) to head (22140b9).
Report is 1 commits behind head on release-20.0.

Files with missing lines	Patch %	Lines
go/vt/vttablet/tabletserver/repltracker/reader.go	66.66%	2 Missing ⚠️

Additional details and impacted files

@@                Coverage Diff                @@
##           release-20.0   #18452       +/-   ##
=================================================
+ Coverage              0   66.42%   +66.42%     
=================================================
  Files                 0     1543     +1543     
  Lines                 0   244949   +244949     
=================================================
+ Hits                  0   162696   +162696     
- Misses                0    82253    +82253     

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