do not contaminate web.log with bg process logs #4049

Job	Run time
build-and-check	2m 56s
test-common	51s
test-backend	42s
test-web	41s
test-npm-app	51s
test-integration-.agents	48s
test-.agents	41s
test-cli	42s
test-packages/agent-runtime	58s
test-integration-packages/agent-runtime	47s
test-integration-web	49s
test-integration-npm-app	46s
test-integration-backend	51s
test-integration-common	41s
test-integration-cli	42s
	13m 46s

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