feat(loader): Sync loader with Sentry template

[AbhiPrasad]

As per #6990 the loader in the JS monorepo and sentry template has drifted apart. This syncs them together (validated by the integration tests in the JS monorepo).

PR in Sentry repo: getsentry/sentry#43880

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	19.87 KB (added)
@sentry/browser - ES5 CDN Bundle (minified)	61.57 KB (added)
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	18.54 KB (added)
@sentry/browser - ES6 CDN Bundle (minified)	54.88 KB (added)
@sentry/browser - Webpack (gzipped + minified)	20.29 KB (added)
@sentry/browser - Webpack (minified)	66.37 KB (added)
@sentry/react - Webpack (gzipped + minified)	20.31 KB (added)
@sentry/nextjs Client - Webpack (gzipped + minified)	47.6 KB (added)
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	26.79 KB (added)
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	25.08 KB (added)
@sentry/replay ES6 CDN Bundle (gzipped + minified)	44.17 KB (added)
@sentry/replay - Webpack (gzipped + minified)	38.92 KB (added)
@sentry/browser + @sentry/tracing + @sentry/replay - ES6 CDN Bundle (gzipped + minified)	61.52 KB (added)