[slack-19.0]:backport: Fix data race in keyspace event watcher (#16683)

[tanjinx]

Description

backport:

• Fix data race in keyspace event watcher vitessio/vitess#16683

Related Issue(s)

Checklist

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

Deployment Notes

AI Disclosure

[salesforce-cla]

Thanks for the contribution! Before we can merge this, we need @GuptaManan100 to sign the Salesforce Inc. Contributor License Agreement.