feat(v8/tracing): Delete BrowserTracing class (#10919)

With this PR and
#10918 merged, we can
move all of the browser tracing related code into `@sentry/browser`.
That will allow us to delete `@sentry-internal/tracing` and stop
publishing it.

ref #9885

Author: AbhiPrasad

dev-packages/browser-integration-tests/suites/tracing/browserTracingIntegrationShim/test.ts

@@ -30,7 +30,7 @@ sentryTest(
 
     expect(requestCount).toBe(0);
     expect(consoleMessages).toEqual([
-      'You are using new BrowserTracing() even though this bundle does not include tracing.',
+      'You are using browserTracingIntegration() even though this bundle does not include tracing.',
     ]);
   },
 );

packages/integration-shims/src/BrowserTracing.ts

@@ -9,7 +9,7 @@ import { consoleSandbox } from '@sentry/utils';
 export const browserTracingIntegrationShim = defineIntegration((_options?: unknown) => {
   consoleSandbox(() => {
     // eslint-disable-next-line no-console
-    console.warn('You are using new BrowserTracing() even though this bundle does not include tracing.');
+    console.warn('You are using browserTracingIntegration() even though this bundle does not include tracing.');
   });
 
   return {