[release-18.0] Fix deadlock between health check and topology watcher (#16995)

[vitess-bot]

Description

This is a backport of #16995

[vitess-bot]

Hello @GuptaManan100, there are conflicts in this backport.

Please address them in order to merge this Pull Request. You can execute the snippet below to reset your branch and resolve the conflict manually.

Make sure you replace origin by the name of the vitessio/vitess remote

git fetch --all
gh pr checkout 17007 -R vitessio/vitess
git reset --hard origin/release-18.0
git cherry-pick -m 1 c1603c0c66cd8256022f6f40cc655c64aef90c7b

[vitess-bot]

Review Checklist

Hello reviewers! 👋 Please follow this checklist when reviewing this Pull Request.

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