improve: health probes showcase & docs to operations #6924

Job	Run time
sample_operators_tests (sample-operators/webpage)	3m 10s
sample_operators_tests (sample-operators/leader-election)	3m 36s
sample_operators_tests (sample-operators/tomcat-operator)	2m 52s
sample_operators_tests (sample-operators/operations)	8m 26s
sample_operators_tests (sample-operators/mysql-schema)	2m 44s
	20m 48s

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