ref(astro): Streamline how we add browser tracing

[mydea]

We should wait for #10243 to merge this, as otherwise we'll get a deprecation/eslint error there.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	77.62 KB (0%)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	68.88 KB (0%)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	72.77 KB (0%)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	62.52 KB (0%)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	32.89 KB (0%)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.16 KB (0%)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.16 KB (0%)
@sentry/browser - Webpack (gzipped)	22.51 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	75.21 KB (0%)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	66.83 KB (0%)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	32.68 KB (0%)
@sentry/browser - ES6 CDN Bundle (gzipped)	24.23 KB (0%)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	210.56 KB (0%)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	98.54 KB (0%)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	72.52 KB (0%)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	35.73 KB (0%)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	69.3 KB (0%)
@sentry/react - Webpack (gzipped)	22.55 KB (0%)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	85.88 KB (0%)
@sentry/nextjs Client - Webpack (gzipped)	50.01 KB (0%)
@sentry-internal/feedback - Webpack (gzipped)	17.14 KB (0%)