feat(core): Track shake to report integration usage (#5929)

* feat(core): Track shake to report integration usage

Add a lazy-loaded ShakeToReport marker integration to track when the
shake-to-report feedback feature is enabled, following the same pattern
used by AutoInjectMobileFeedback and other feedback marker integrations.

Closes #5897

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* Fix lint issue

---------

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: antonis

packages/core/src/js/feedback/FeedbackWidgetManager.tsx

@@ -5,6 +5,7 @@ import {
   lazyLoadAutoInjectFeedbackButtonIntegration,
   lazyLoadAutoInjectFeedbackIntegration,
   lazyLoadAutoInjectScreenshotButtonIntegration,
+  lazyLoadShakeToReportIntegration,
 } from './lazy';
 import { startShakeListener, stopShakeListener } from './ShakeToReportBug';
 
@@ -146,6 +147,7 @@ let _imperativeShakeListenerStarted = false;
 
 const enableFeedbackOnShake = (): void => {
   lazyLoadAutoInjectFeedbackIntegration();
+  lazyLoadShakeToReportIntegration();
   if (!_imperativeShakeListenerStarted) {
     _imperativeShakeListenerStarted = startShakeListener(showFeedbackWidget);
   }

packages/core/src/js/feedback/FeedbackWidgetProvider.tsx

@@ -37,6 +37,7 @@ import {
   getScreenshotButtonOptions,
   isShakeToReportEnabled,
 } from './integration';
+import { lazyLoadShakeToReportIntegration } from './lazy';
 import { ScreenshotButton } from './ScreenshotButton';
 import { startShakeListener, stopShakeListener } from './ShakeToReportBug';
 import { isModalSupported, isNativeDriverSupportedForColorAnimations } from './utils';
@@ -123,6 +124,7 @@ export class FeedbackWidgetProvider extends React.Component<FeedbackWidgetProvid
     });
 
     if (isShakeToReportEnabled()) {
+      lazyLoadShakeToReportIntegration();
       this._startedShakeListener = startShakeListener(showFeedbackWidget);
     }
   }

packages/core/src/js/feedback/lazy.ts

@@ -39,6 +39,19 @@ export function lazyLoadAutoInjectFeedbackButtonIntegration(): void {
   }
 }
 
+export const SHAKE_TO_REPORT_INTEGRATION_NAME = 'ShakeToReport';
+
+/**
+ * Lazy loads the shake to report integration if it is not already loaded.
+ */
+export function lazyLoadShakeToReportIntegration(): void {
+  const integration = getClient()?.getIntegrationByName(SHAKE_TO_REPORT_INTEGRATION_NAME);
+  if (!integration) {
+    // Lazy load the integration to track usage
+    getClient()?.addIntegration({ name: SHAKE_TO_REPORT_INTEGRATION_NAME });
+  }
+}
+
 export const AUTO_INJECT_SCREENSHOT_BUTTON_INTEGRATION_NAME = 'AutoInjectMobileScreenshotButton';
 
 /**