chore(integration-tests): Update Playwright to 1.27.1

[onurtemizkan]

Updated playwright and @playwright/test versions from 1.17 to 1.27, which will make it easier to test client-side HTTP headers for #6500.

There seem to be minor changes in Chromium stacktraces in newer versions. This PR also updates them.

There were also a few TS errors, which were breaking local test runs (but not CI). Also fixed them.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	19.71 KB (+0.01% 🔺)
@sentry/browser - ES5 CDN Bundle (minified)	61.11 KB (0%)
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	18.5 KB (-0.02% 🔽)
@sentry/browser - ES6 CDN Bundle (minified)	54.64 KB (0%)
@sentry/browser - Webpack (gzipped + minified)	20.28 KB (0%)
@sentry/browser - Webpack (minified)	66.33 KB (0%)
@sentry/react - Webpack (gzipped + minified)	20.3 KB (0%)
@sentry/nextjs Client - Webpack (gzipped + minified)	47.5 KB (+0.42% 🔺)
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	26.7 KB (-0.01% 🔽)
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	25.15 KB (+0.01% 🔺)
@sentry/replay ES6 CDN Bundle (gzipped + minified)	41.73 KB (-0.01% 🔽)
@sentry/replay - Webpack (gzipped + minified)	38 KB (0%)