test(browser): Fix flaky browser integration test for profiles

[mydea]

This updates a browser integration test to make it less flaky. Instead of first calling await page.goto(...) we now combine this with getMultipleSentryEnvelopeRequests to avoid possible race conditions.

Fixes#20585
Fixes#20524
Fixes#20612

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[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	26.16 kB	-	-
@sentry/browser - with treeshaking flags	24.63 kB	-	-
@sentry/browser (incl. Tracing)	44.11 kB	-	-
@sentry/browser (incl. Tracing + Span Streaming)	46.16 kB	-	-
@sentry/browser (incl. Tracing, Profiling)	49.06 kB	-	-
@sentry/browser (incl. Tracing, Replay)	83.46 kB	-	-
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	72.94 kB	-	-
@sentry/browser (incl. Tracing, Replay with Canvas)	88.14 kB	-	-
@sentry/browser (incl. Tracing, Replay, Feedback)	100.79 kB	-	-
@sentry/browser (incl. Feedback)	43.4 kB	-	-
@sentry/browser (incl. sendFeedback)	30.96 kB	-	-
@sentry/browser (incl. FeedbackAsync)	36.14 kB	-	-
@sentry/browser (incl. Metrics)	27.44 kB	-	-
@sentry/browser (incl. Logs)	27.59 kB	-	-
@sentry/browser (incl. Metrics & Logs)	28.28 kB	-	-
@sentry/react	27.9 kB	-	-
@sentry/react (incl. Tracing)	46.35 kB	-	-
@sentry/vue	31.03 kB	-	-
@sentry/vue (incl. Tracing)	45.95 kB	-	-
@sentry/svelte	26.18 kB	-	-
CDN Bundle	28.84 kB	-	-
CDN Bundle (incl. Tracing)	46.71 kB	-	-
CDN Bundle (incl. Logs, Metrics)	30.25 kB	-	-
CDN Bundle (incl. Tracing, Logs, Metrics)	47.8 kB	-	-
CDN Bundle (incl. Replay, Logs, Metrics)	69.34 kB	-	-
CDN Bundle (incl. Tracing, Replay)	83.88 kB	-	-
CDN Bundle (incl. Tracing, Replay, Logs, Metrics)	84.94 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback)	89.69 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics)	90.78 kB	-	-
CDN Bundle - uncompressed	84.55 kB	-	-
CDN Bundle (incl. Tracing) - uncompressed	139.68 kB	-	-
CDN Bundle (incl. Logs, Metrics) - uncompressed	88.75 kB	-	-
CDN Bundle (incl. Tracing, Logs, Metrics) - uncompressed	143.14 kB	-	-
CDN Bundle (incl. Replay, Logs, Metrics) - uncompressed	212.71 kB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	257.49 kB	-	-
CDN Bundle (incl. Tracing, Replay, Logs, Metrics) - uncompressed	260.93 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	271.18 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback, Logs, Metrics) - uncompressed	274.62 kB	-	-
@sentry/nextjs (client)	48.84 kB	-	-
@sentry/sveltekit (client)	44.56 kB	-	-
@sentry/node-core	58.96 kB	+0.02%	+8 B 🔺
@sentry/node	170.25 kB	+0.01%	+8 B 🔺
@sentry/node - without tracing	96.82 kB	+0.01%	+8 B 🔺
@sentry/aws-serverless	113.69 kB	+0.03%	+33 B 🔺
@sentry/cloudflare (withSentry) - minified	164.13 kB	-	-
@sentry/cloudflare (withSentry)	415.2 kB	-	-

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