ref(core): Refactor core integrations to functional style

[mydea]

Also make a small adjustment to the legacy converter util to ensure setupOnce() is callable with or without arguments, to remain stable.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	75.35 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	66.75 KB (-0.02% 🔽)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	60.34 KB (-0.01% 🔽)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	31.41 KB (-0.04% 🔽)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	30.02 KB (-0.02% 🔽)
@sentry/browser - Webpack (gzipped)	21.71 KB (-0.03% 🔽)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	72.73 KB (-0.02% 🔽)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	64.44 KB (-0.04% 🔽)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	30.73 KB (-0.02% 🔽)
@sentry/browser - ES6 CDN Bundle (gzipped)	22.82 KB (+0.14% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	202.43 KB (-0.08% 🔽)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	92.55 KB (-0.14% 🔽)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	67.61 KB (-0.18% 🔽)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	33.59 KB (+0.03% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	67.12 KB (-0.01% 🔽)
@sentry/react - Webpack (gzipped)	21.75 KB (-0.03% 🔽)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	83.9 KB (-0.02% 🔽)
@sentry/nextjs Client - Webpack (gzipped)	48.57 KB (-0.03% 🔽)
@sentry-internal/feedback - Webpack (gzipped)	16.35 KB (0%)