fix(test): Fix flaky browser integration tests.

Author: onurtemizkan

dev-packages/browser-integration-tests/suites/integrations/Breadcrumbs/dom/click/test.ts

@@ -76,8 +76,8 @@ sentryTest(
 
     const promise = getFirstSentryEnvelopeRequest<Event>(page);
 
-    await page.goto(url);
-    await page.locator('#annotated-button').click();
+    await Promise.all([page.goto(url), page.locator('#annotated-button').click()]);
+
     await page.evaluate('Sentry.captureException("test exception")');
 
     const eventData = await promise;

dev-packages/browser-integration-tests/suites/public-api/startSpan/basic/subject.js

@@ -6,4 +6,6 @@ async function run() {
   });
 }
 
-run();
+(async () => {
+  await run();
+})();

dev-packages/browser-integration-tests/suites/replay/errorResponse/test.ts

@@ -23,9 +23,8 @@ sentryTest('should stop recording after receiving an error response', async ({ g
   });
 
   const url = await getLocalTestPath({ testDir: __dirname });
-  await page.goto(url);
+  await Promise.all([page.goto(url), waitForReplayRequest(page)]);
 
-  await waitForReplayRequest(page);
   await page.locator('button').click();
 
   expect(called).toBe(1);