[release-1.19] Add MachineHealthCheck for control plane to private cluster e2e template

[k8s-infra-cherrypick-robot]

This is an automated cherry-pick of #5801

/assign nojnhuh

NONE

[k8s-ci-robot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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[nojnhuh]

/close

I had invoked the bot on the original PR before we stopped maintaining the 1.19 branch.

[k8s-ci-robot]

@nojnhuh: Closed this PR.

In response to this:

/close

I had invoked the bot on the original PR before we stopped maintaining the 1.19 branch.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 52.55%. Comparing base (8d7902a) to head (add5be2).
⚠️ Report is 1 commits behind head on release-1.19.

Additional details and impacted files

@@              Coverage Diff              @@
##           release-1.19    #5917   +/-   ##
=============================================
  Coverage         52.54%   52.55%           
=============================================
  Files               273      273           
  Lines             29493    29493           
=============================================
+ Hits              15498    15500    +2     
+ Misses            13193    13191    -2     
  Partials            802      802           

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