improve: health probes showcase & docs to operations #6877

Job	Run time
sample_operators_tests (sample-operators/mysql-schema)	2m 40s
sample_operators_tests (sample-operators/leader-election)	3m 19s
sample_operators_tests (sample-operators/webpage)	3m 17s
sample_operators_tests (sample-operators/tomcat-operator)	2m 43s
sample_operators_tests (sample-operators/operations)	11m 8s
	23m 7s

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