build(replay): Adjust type declaration output directory

[Lms24]

This PR follows up with a small change on top of #6343 to further align the build directory. Previously, types were built into build/npm/types/src/index.d.ts. The src sub-directory shouldn't be in there, so this PR fixes that by removing some leftover properties in the main tsconfig.json which caused this sub-directory to appear.

This PR also removes a few additional unnecessary properties, such as types which we only need in tsconfig.test.json.

ref: #6280

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	19.57 KB (-0.01% 🔽)
@sentry/browser - ES5 CDN Bundle (minified)	60.59 KB (0%)
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	18.36 KB (+0.02% 🔺)
@sentry/browser - ES6 CDN Bundle (minified)	54.15 KB (0%)
@sentry/browser - Webpack (gzipped + minified)	20.12 KB (0%)
@sentry/browser - Webpack (minified)	65.75 KB (0%)
@sentry/react - Webpack (gzipped + minified)	20.14 KB (0%)
@sentry/nextjs Client - Webpack (gzipped + minified)	45.99 KB (0%)
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	26.45 KB (-0.01% 🔽)
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	24.88 KB (+0.02% 🔺)
@sentry/replay index.js	37.2 KB (0%)
@sentry/replay - Webpack (gzipped + minified)	37.17 KB (0%)
@sentry/replay - Webpack (minified)	124.99 KB (0%)