feat(sdk): Add a timeOrigin.mode tag (#24901)

- This is so we can track how often we're changing timeOrigin to get a
  better calculation

src/sentry/static/sentry/app/bootstrap/initializeSdk.tsx

@@ -3,6 +3,7 @@ import {ExtraErrorData} from '@sentry/integrations';
 import * as Sentry from '@sentry/react';
 import SentryRRWeb from '@sentry/rrweb';
 import {Integrations} from '@sentry/tracing';
+import {_browserPerformanceTimeOriginMode} from '@sentry/utils';
 
 import {DISABLE_RR_WEB, SPA_DSN} from 'app/constants';
 import {Config} from 'app/types';
@@ -79,6 +80,13 @@ export function initializeSdk(config: Config, {routes}: {routes?: Function} = {}
     tracesSampleRate,
   });
 
+  // Track timeOrigin Selection by the SDK to see if it improves transaction durations
+  Sentry.addGlobalEventProcessor((event: Sentry.Event, _hint?: Sentry.EventHint) => {
+    event.tags = event.tags || {};
+    event.tags['timeOrigin.mode'] = _browserPerformanceTimeOriginMode;
+    return event;
+  });
+
   if (userIdentity) {
     Sentry.setUser(userIdentity);
   }