Deprecate old reparent metrics and replace with new ones

[GuptaManan100]

Description

This PR is a continuation of the work done in #15994 as requested in #15994 (review).

This PR makes the same changes as in #15994 for reparent metrics wherein we keep the deprecated name for the metrics, but also register them with the new name to ensure backward compatibility before we remove the metrics.

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 68.24%. Comparing base (0a86449) to head (37a7847).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #16031   +/-   ##
=======================================
  Coverage   68.23%   68.24%           
=======================================
  Files        1541     1541           
  Lines      197115   197125   +10     
=======================================
+ Hits       134503   134529   +26     
+ Misses      62612    62596   -16     

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