Log some web api analytics to debug prod events #5289

Job	Run time
build-and-check	2m 35s
test-integration-common	45s
test-integration-packages/agent-runtime	40s
test-integration-.agents	40s
test-integration-cli	37s
test-integration-packages/billing	38s
test-integration-packages/internal	47s
test-packages/agent-runtime	51s
test-packages/internal	48s
test-common	39s
test-cli	1m 13s
test-sdk	45s
test-web	42s
test-.agents	37s
test-integration-web	39s
test-integration-sdk	44s
test-packages/billing	38s
	14m 18s

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