ref(replay): Extract some more handlers out into functional style

[mydea]

Extract some remaining handler stuff out into a functional style.
Also extract the global listener stuff (=things that cannot be reverted) out into a dedicated funtion.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser - ES5 CDN Bundle (gzipped + minified)	19.83 KB (+0.05% 🔺)
@sentry/browser - ES5 CDN Bundle (minified)	61.48 KB (+0.03% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped + minified)	18.5 KB (+0.04% 🔺)
@sentry/browser - ES6 CDN Bundle (minified)	54.79 KB (+0.03% 🔺)
@sentry/browser - Webpack (gzipped + minified)	20.22 KB (+0.05% 🔺)
@sentry/browser - Webpack (minified)	66.19 KB (+0.03% 🔺)
@sentry/react - Webpack (gzipped + minified)	20.25 KB (+0.04% 🔺)
@sentry/nextjs Client - Webpack (gzipped + minified)	47.48 KB (+0.02% 🔺)
@sentry/browser + @sentry/tracing - ES5 CDN Bundle (gzipped + minified)	26.75 KB (+0.05% 🔺)
@sentry/browser + @sentry/tracing - ES6 CDN Bundle (gzipped + minified)	25.03 KB (+0.03% 🔺)
@sentry/replay ES6 CDN Bundle (gzipped + minified)	43.2 KB (-0.14% 🔽)
@sentry/replay - Webpack (gzipped + minified)	37.93 KB (-0.3% 🔽)
@sentry/browser + @sentry/tracing + @sentry/replay - ES6 CDN Bundle (gzipped + minified)	60.55 KB (+0.06% 🔺)