Fix deadlock in messager and health streamer

[GuptaManan100]

Description

This PR fixes the deadlocks in messager and health streamer as pointed out in #17229.

The fix to the deadlock for both the cases was to use two different mutexes. One that only protects against calling setup functions like Open and Close concurrently, and the other one that actually protects the fields. This helps in removing the deadlock since the function that runs on a broadcast from the schema engine would acquire a different mutex than the call to Close.

Related Issue(s)

• Fixes #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

Attention: Patch coverage is 89.18919% with 4 lines in your changes missing coverage. Please review.

Project coverage is 67.39%. Comparing base (c72bbdc) to head (3901fc2). Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
go/vt/vttablet/tabletserver/health_streamer.go	82.60%	4 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #17230 +/- ## ======================================= Coverage 67.39% 67.39% ======================================= Files 1570 1570 Lines 252903 252912 +9 ======================================= + Hits 170438 170461 +23 + Misses 82465 82451 -14 ```

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[derekperkins]

For some historical context, when the original code was written, defer still had a somewhat significant penalty, hence the lack of defer mu.Unlock. That was resolved in upstream Go in v1.14.