Fix: errant GTID in health streamer

[GuptaManan100]

Description

This PR fixes the health streamer issue described in #13182. This is a partial back port of #13121

Related Issue(s)

• Bug Report: Errant gtid possible in schema tracking in health streamer #13182

Checklist

• "Backport to:" labels have been added if this change should be back-ported
• Tests were added or are not required
• Did the new or modified tests pass consistently locally and on the CI
• Documentation was added or is not required

Deployment Notes

[vitess-bot]

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[deepthi]

I see that you've followed the same pattern as replTracker. I can't say that I like this spreading around of primary/serving state between the various sub-structs of tmState, but there doesn't seem to be any better way of doing it.

[deepthi]

unit_race is actually failing. It's a good thing we run our unit tests with the race detector 😅

[GuptaManan100]

The upgrade downgrade failures look unrelated. I will investigate them separately.

[vitess-bot]

I was unable to backport this Pull Request to the following branches: release-14.0, release-15.0.

[GuptaManan100]

@frouioui is taking a look at the upgrade downgrade failures