Detailed check for health check endpoint '/readyz'

[anencore94]

/kind feature

Describe the solution you'd like
[A clear and concise description of what you want to happen.]

On #1934, we issue there might need to determine whether the katib controller is ready or not more sophistically.
But, for now, I don't have any idea for what we need to check necessary, and how often we need to check it.

Ref)

• [feat] health check for katib-controller #1934 (comment)
• [feat] health check for katib-controller #1934 (comment)

Anything else you would like to add:
[Miscellaneous information that will assist in solving the issue.]

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[github-actions]

This issue has been automatically marked as stale because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions.

[tenzen-y]

/lifecycle frozen