test(replay): Add integration tests for capturing console logs for replays

[mydea]

Extracted this out from #7916, as it is flaky - need to figure out why...

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	21.02 KB (+0.19% 🔺)
@sentry/browser - ES5 CDN Bundle (minified)	65.65 KB (+0.24% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	19.56 KB (+0.18% 🔺)
@sentry/browser - ES6 CDN Bundle (minified)	58.1 KB (+0.27% 🔺)
@sentry/browser - Webpack (gzipped + minified)	21.16 KB (+0.2% 🔺)
@sentry/browser - Webpack (minified)	69.06 KB (+0.23% 🔺)
@sentry/react - Webpack (gzipped + minified)	21.18 KB (+0.2% 🔺)
@sentry/nextjs Client - Webpack (gzipped + minified)	49.03 KB (+0.09% 🔺)
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	28.58 KB (+0.13% 🔺)
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	26.81 KB (+0.14% 🔺)
@sentry/replay ES6 CDN Bundle (gzipped + minified)	46.04 KB (+1.54% 🔺)
@sentry/replay - Webpack (gzipped + minified)	39.92 KB (+1.64% 🔺)
@sentry/browser + @sentry/tracing + @sentry/replay - ES6 CDN Bundle (gzipped + minified)	64.9 KB (+1.06% 🔺)
@sentry/browser + @sentry/replay - ES6 CDN Bundle (gzipped + minified)	57.88 KB (+1.2% 🔺)