chore(ts): Add TS3.8 compile test

[krystofwoldrich]

• relatest to fix(ts): Publish downleveled TS3.8 types, fix types path #8954

Adds project that fails to compile if downleveled types of its deps are not TS3.8 compatible.

[krystofwoldrich]

It's the same test as we have in sentry-react-native, there it's a bit simple as it's only one project. If there is better solution for monorepos I'm open to ideas.

[lforst]

Can we do this as an E2E test instead? I like the idea tho.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	75.38 KB (0%)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	31.31 KB (0%)
@sentry/browser - Webpack (gzipped)	21.91 KB (0%)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	70.16 KB (0%)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	28.5 KB (-0.01% 🔽)
@sentry/browser - ES6 CDN Bundle (gzipped)	20.59 KB (-0.01% 🔽)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	221.75 KB (0%)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	86.28 KB (0%)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	61.13 KB (0%)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	31.37 KB (0%)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	75.4 KB (0%)
@sentry/react - Webpack (gzipped)	21.94 KB (0%)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	93.27 KB (0%)
@sentry/nextjs Client - Webpack (gzipped)	50.88 KB (0%)

[krystofwoldrich]

The test passed, it's ready for another review.