Remove internal API status from get/setDistinctId #5195

Job	Run time
system-test (sentry-samples-spring-boot-jakarta-opentelemetry-noagent, false, true)	5m 22s
system-test (sentry-samples-spring-boot-jakarta, false, true)	2m 47s
system-test (sentry-samples-console, false, true)	1m 39s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, true)	5m 28s
system-test (sentry-samples-spring-boot-4, false, true)	3m 16s
system-test (sentry-samples-spring-boot-opentelemetry-noagent, false, true)	5m 12s
system-test (sentry-samples-log4j2, false, true)	1m 32s
system-test (sentry-samples-spring-boot-webflux, false, true)	3m 1s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, false)	5m 44s
system-test (sentry-samples-spring-boot-opentelemetry, true, false)	5m 33s
system-test (sentry-samples-spring-boot-4-webflux, false, true)	2m 37s
system-test (sentry-samples-spring-boot-webflux-jakarta, false, true)	3m 28s
system-test (sentry-samples-spring-boot-jakarta-opentelemetry, true, false)	5m 49s
system-test (sentry-samples-spring-boot-opentelemetry, true, true)	5m 21s
system-test (sentry-samples-spring-boot-4-opentelemetry, true, true)	5m 43s
system-test (sentry-samples-jul, false, true)	1m 26s
system-test (sentry-samples-logback, false, true)	1m 29s
system-test (sentry-samples-spring-boot, false, true)	3m 5s
system-test (sentry-samples-spring-jakarta, false, true)	2m 17s
	1h 10m 49s

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