Fix data race in Schema Engine

[harshit-gangal]

Description

This PR fixes the data race seen in schema engine.
This was caused by making changes in the PR #17855 which does not take lock on calling the reload method causing multiple data race.

This also reverts a change made in PR to fix partial data race #17914

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

[vitess-bot]

Review Checklist

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 67.56%. Comparing base (74d9949) to head (4953597).
Report is 5 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #17921   +/-   ##
=======================================
  Coverage   67.56%   67.56%           
=======================================
  Files        1597     1597           
  Lines      259775   259782    +7     
=======================================
+ Hits       175509   175528   +19     
+ Misses      84266    84254   -12     

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