Expose the default `HealthCheckUpdateHandler` #11763

Job	Run time
flaky-tests	14m 30s
build-ubicloud-standard-8-jdk-21-snapshot-blockhound	25m 28s
build-macos-12-jdk-21	1h 6m 15s
lint	13m 10s
build-windows-latest-jdk-21	1h 5m 18s
build-ubicloud-standard-8-jdk-8	16m 11s
build-ubicloud-standard-8-jdk-11	11m 31s
site	8m 36s
build-ubicloud-standard-8-jdk-17-leak	19m 58s
build-ubicloud-standard-8-jdk-17-min-java-11	19m 14s
build-ubicloud-standard-8-jdk-17-min-java-17-coverage	25m 7s
	4h 45m 18s

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