server: Remove deprecated NewZapCoreLoggerBuilder

[ivanvc]

This pull request removes the deprecated NewZapCoreLoggerBuilder function.

Please read https://github.com/etcd-io/etcd/blob/main/CONTRIBUTING.md#contribution-flow.

[ivanvc]

I will add it to the CHANGELOG once the PR is merged.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 68.90%. Comparing base (dd6791c) to head (8b99f8e).
Report is 2 commits behind head on main.

Additional details and impacted files

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

... and 20 files with indirect coverage changes

@@            Coverage Diff             @@
##             main   #19403      +/-   ##
==========================================
- Coverage   68.94%   68.90%   -0.05%     
==========================================
  Files         420      420              
  Lines       35759    35757       -2     
==========================================
- Hits        24655    24637      -18     
- Misses       9679     9699      +20     
+ Partials     1425     1421       -4     

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[ivanvc]

/retest

[k8s-ci-robot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: ahrtr, ivanvc

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[ahrtr]

/cherry-pick release-3.6

[k8s-infra-cherrypick-robot]

@ahrtr: new pull request created: #19404

In response to this:

/cherry-pick release-3.6

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