Fix potential deadlock in health streamer

[GuptaManan100]

Description

While we fixed a couple of deadlocks in https://github.com/vitessio/vitess/pull/17230, one was left pending. It was found while testing for deadlocks in https://github.com/vitessio/vitess/pull/17238.

The deadlock is similar to the ones fixed in https://github.com/vitessio/vitess/pull/17230, it was occurring between MakePrimary and the reload. The fix employed is to let go of the lock once it is not required instead of defering its unlocking.

Related Issue(s)

• 17229

Checklist

• [x] "Backport to:" labels have been added if this change should be back-ported to release branches
• [x] If this change is to be back-ported to previous releases, a justification is included in the PR description
• [x] Tests were added or are not required
• [x] Did the new or modified tests pass consistently locally and on CI?
• [x] Documentation was added or is not required

Deployment Notes

[vitess-bot[bot]]

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[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 67.39%. Comparing base (2c6e053) to head (eadb128). Report is 5 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #17261 +/- ## ======================================= Coverage 67.39% 67.39% ======================================= Files 1570 1573 +3 Lines 252970 253060 +90 ======================================= + Hits 170484 170559 +75 - Misses 82486 82501 +15 ```

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[mdlayher]

If we're able, you could consider swapping this for the fairly new atomic.Bool in Go to eliminate this lock all together!

[arthurschreiber]

If we're able, you could consider swapping this for the fairly new atomic.Bool in Go to eliminate this lock all together!

I don't think that's possible here, because we depend on a consistent view over multiple fields (isServingPrimary, state).

[mdlayher]

If a consistent view over multiple fields is necessary then https://pkg.go.dev/sync/atomic#Pointer with a struct is also an option. No strong feelings, just wanted to offer a suggestion to eliminate the lock.