ref(browser): Refactor sentry breadcrumb to use hook

[mydea]

Noticed that this is a bit tightly coupled in the browser client, and could be simplified by using a hook.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	75.23 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	31.22 KB (+0.06% 🔺)
@sentry/browser - Webpack (gzipped)	21.86 KB (+0.05% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	69.76 KB (+0.02% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	28.18 KB (-0.11% 🔽)
@sentry/browser - ES6 CDN Bundle (gzipped)	20.19 KB (+0.02% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	220.02 KB (-0.02% 🔽)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	84.85 KB (-0.05% 🔽)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	59.84 KB (-0.04% 🔽)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	31.07 KB (-0.11% 🔽)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	75.25 KB (+0.01% 🔺)
@sentry/react - Webpack (gzipped)	21.89 KB (+0.06% 🔺)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	93.09 KB (+0.05% 🔺)
@sentry/nextjs Client - Webpack (gzipped)	50.75 KB (+0.04% 🔺)