[release-3.6] server: Remove deprecated NewZapCoreLoggerBuilder

[k8s-infra-cherrypick-robot]

This is an automated cherry-pick of #19403

/assign ahrtr

[k8s-ci-robot]

Hi @k8s-infra-cherrypick-robot. Thanks for your PR.

I'm waiting for a etcd-io member to verify that this patch is reasonable to test. If it is, they should reply with /ok-to-test on its own line. Until that is done, I will not automatically test new commits in this PR, but the usual testing commands by org members will still work. Regular contributors should join the org to skip this step.

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[ahrtr]

/ok-to-test

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 68.93%. Comparing base (2feb5a2) to head (f1095ba).
Report is 2 commits behind head on release-3.6.

Additional details and impacted files

Files with missing lines	Coverage Δ
server/embed/config_logging.go	52.17% <ø> (+0.64%)	⬆️

... and 22 files with indirect coverage changes

@@             Coverage Diff              @@
##           release-3.6   #19404   +/-   ##
============================================
  Coverage        68.92%   68.93%           
============================================
  Files              420      420           
  Lines            35759    35757    -2     
============================================
  Hits             24648    24648           
+ Misses            9692     9685    -7     
- Partials          1419     1424    +5     

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[ivanvc]

LGTM on green.

[k8s-ci-robot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: ahrtr, ivanvc, k8s-infra-cherrypick-robot

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