ref(browser): Update browser metrics to avoid deprecations

[mydea]

This rewrites browser metrics to:

1. Accept spans instead of transactions
2. Use the new performance APIs instead of the old ones

The only thing I left for now is the tags, which we can get rid of separately: #10823

Part of #10900

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	77.51 KB (+0.17% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	68.73 KB (+0.21% 🔺)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	72.63 KB (+0.19% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	62.29 KB (+0.23% 🔺)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	32.96 KB (+0.39% 🔺)
@sentry/browser (incl. browserTracingIntegration) - Webpack (gzipped)	32.96 KB (+0.39% 🔺)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.36 KB (+0.06% 🔺)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.37 KB (+0.06% 🔺)
@sentry/browser - Webpack (gzipped)	22.57 KB (+0.06% 🔺)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	75.55 KB (+0.17% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	67.15 KB (+0.15% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	33 KB (+0.28% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped)	23.98 KB (+0.04% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	210.65 KB (+0.06% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	99.45 KB (+0.12% 🔺)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	71.67 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	36.18 KB (+0.36% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	68.98 KB (+0.16% 🔺)
@sentry/react - Webpack (gzipped)	22.6 KB (+0.06% 🔺)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	85.43 KB (+0.16% 🔺)
@sentry/nextjs Client - Webpack (gzipped)	49.83 KB (+0.26% 🔺)
@sentry-internal/feedback - Webpack (gzipped)	17.41 KB (0%)