Ensure tests cover non-error timber tags #5755

Job	Run time
system-test (sentry-samples-spring-boot, false, true)	2m 18s
system-test (sentry-samples-spring-boot-opentelemetry-noagent, false, true)	4m 21s
system-test (sentry-samples-spring-boot-webflux, false, true)	2m 10s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry-noagent, false, true)	4m 30s
system-test (sentry-samples-spring-boot-opentelemetry, true, true)	4m 33s
system-test (sentry-samples-spring-boot-webflux-jakarta, false, true)	2m 8s
system-test (sentry-samples-logback, false, true)	55s
system-test (sentry-samples-console, false, true)	1m 1s
system-test (sentry-samples-jul, false, true)	1m 3s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, false)	4m 45s
system-test (sentry-samples-log4j2, false, true)	1m 2s
system-test (sentry-samples-spring-boot-opentelemetry, true, false)	4m 28s
system-test (sentry-samples-spring-boot-jakarta, false, true)	3m 40s
system-test (sentry-samples-spring-boot-4, false, true)	1m 35s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, false)	4m 36s
system-test (sentry-samples-spring, false, true)	1m 51s
system-test (sentry-samples-spring-7, false, true)	1m 40s
system-test (sentry-samples-spring-boot-4-webflux, false, true)	2m 13s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, true)	4m 37s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, true)	4m 36s
system-test (sentry-samples-spring-jakarta, false, true)	1m 40s
	59m 42s

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