feat: probe use built-in, discarded healthcheck.sh

[drivebyer]

Description

#443, #766

Type of change

• New feature (non-breaking change which adds functionality)

Checklist

• Tests have been added/modified and all tests pass.
• Functionality/bugs have been confirmed to be unchanged or fixed.
• I have performed a self-review of my own code.
• Documentation has been updated or added where necessary.

Additional Context

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 19 lines in your changes are missing coverage. Please review.

Project coverage is 39.75%. Comparing base (d121d86) to head (b43c471).
Report is 36 commits behind head on master.

❗ Current head b43c471 differs from pull request most recent head 700b8dd. Consider uploading reports for the commit 700b8dd to get more accurate results

Files	Patch %	Lines
k8sutils/statefulset.go	0.00%	19 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #907      +/-   ##
==========================================
+ Coverage   35.20%   39.75%   +4.55%     
==========================================
  Files          19       19              
  Lines        3213     2674     -539     
==========================================
- Hits         1131     1063      -68     
+ Misses       2015     1540     -475     
- Partials       67       71       +4     

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