test(web): add unit tests for healthz endpoint #5502

Job	Run time
build-and-check	2m 26s
test-integration-packages/billing	1m 4s
test-integration-cli	40s
test-integration-packages/internal	38s
test-integration-sdk	39s
test-integration-common	37s
test-.agents	39s
test-integration-packages/agent-runtime	47s
test-cli	1m 10s
test-packages/agent-runtime	59s
test-integration-web	38s
test-common	41s
test-packages/billing	42s
test-packages/internal	52s
test-sdk	1m 0s
test-web	1m 12s
	14m 44s

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