feat(logging): Log Timber tag as log attribute #5799

Job	Run time
system-test (sentry-samples-spring-boot-opentelemetry, true, true)	4m 35s
system-test (sentry-samples-spring-boot-opentelemetry-noagent, false, true)	4m 34s
system-test (sentry-samples-spring-boot-jakarta, false, true)	3m 52s
system-test (sentry-samples-spring-boot-webflux-jakarta, false, true)	2m 24s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, false)	4m 51s
system-test (sentry-samples-spring-boot-webflux, false, true)	2m 26s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry-noagent, false, true)	4m 40s
system-test (sentry-samples-spring-boot-opentelemetry, true, false)	4m 32s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, true)	5m 4s
system-test (sentry-samples-console, false, true)	1m 2s
system-test (sentry-samples-spring-boot-4-webflux, false, true)	2m 17s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, true)	4m 51s
system-test (sentry-samples-spring-boot-4, false, true)	2m 13s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, false)	5m 3s
system-test (sentry-samples-spring-jakarta, false, true)	1m 44s
system-test (sentry-samples-jul, false, true)	1m 8s
system-test (sentry-samples-log4j2, false, true)	1m 18s
system-test (sentry-samples-spring, false, true)	1m 59s
system-test (sentry-samples-spring-7, false, true)	2m 7s
system-test (sentry-samples-logback, false, true)	1m 10s
system-test (sentry-samples-spring-boot, false, true)	2m 27s
	1h 4m 17s

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