feat(browser): Export functional integrations & deprecate classes

[mydea]

Also deprecate the Integrations hash in browser SDKs.

I also forgot to add the integrations from @sentry/integrations to the migration.md doc, so adding those as well!

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	77.69 KB (-0.01% 🔽)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	68.95 KB (-0.01% 🔽)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	72.83 KB (-0.01% 🔽)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	62.58 KB (-0.01% 🔽)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	32.97 KB (+0.04% 🔺)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.19 KB (+0.04% 🔺)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.2 KB (+0.03% 🔺)
@sentry/browser - Webpack (gzipped)	22.5 KB (-0.14% 🔽)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	75.43 KB (+0.1% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	67.07 KB (+0.1% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	32.9 KB (+0.24% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped)	24.42 KB (+0.31% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	211.22 KB (+0.09% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	99.21 KB (+0.18% 🔺)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	73.04 KB (+0.25% 🔺)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	35.98 KB (+0.16% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	69.38 KB (+0.04% 🔺)
@sentry/react - Webpack (gzipped)	22.55 KB (-0.11% 🔽)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	86.01 KB (+0.06% 🔺)
@sentry/nextjs Client - Webpack (gzipped)	50.31 KB (+0.11% 🔺)
@sentry-internal/feedback - Webpack (gzipped)	17.14 KB (0%)