feat(logs): Do not send manual log origin #6002

Job	Run time
system-test (sentry-samples-spring-boot-opentelemetry-noagent, false, true)	4m 33s
system-test (sentry-samples-spring-boot-webflux, false, true)	2m 33s
system-test (sentry-samples-spring-boot-opentelemetry, true, true)	4m 48s
system-test (sentry-samples-spring-boot-webflux-jakarta, false, true)	2m 9s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry-noagent, false, true)	4m 49s
system-test (sentry-samples-spring-boot, false, true)	2m 10s
system-test (sentry-samples-console, false, true)	1m 16s
system-test (sentry-samples-spring-boot-jakarta, false, true)	3m 56s
system-test (sentry-samples-jul, false, true)	1m 17s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, false)	4m 58s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, true)	5m 4s
system-test (sentry-samples-log4j2, false, true)	1m 10s
system-test (sentry-samples-logback, false, true)	1m 16s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, false)	4m 55s
system-test (sentry-samples-spring, false, true)	1m 58s
system-test (sentry-samples-spring-7, false, true)	2m 1s
system-test (sentry-samples-spring-boot-opentelemetry, true, false)	4m 41s
system-test (sentry-samples-spring-boot-4, false, true)	2m 2s
system-test (sentry-samples-spring-jakarta, false, true)	2m 4s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, true)	5m 10s
system-test (sentry-samples-spring-boot-4-webflux, false, true)	2m 36s
	1h 5m 26s

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