feat(core): Update Sentry.addBreadcrumb to skip hub

[mydea]

Build on top of #10600, as that relies on this to ensure replay still works.

This basically goes a step further than https://github.com/getsentry/sentry-javascript/pull/10586/files to actually change the implementation to skip the hub completely.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	77.89 KB (-0.25% 🔽)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	69.12 KB (-0.24% 🔽)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	73.05 KB (-0.25% 🔽)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	62.74 KB (-0.31% 🔽)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	33.31 KB (+0.11% 🔺)
@sentry/browser (incl. browserTracingIntegration) - Webpack (gzipped)	33.16 KB (+0.08% 🔺)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.17 KB (+0.04% 🔺)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.16 KB (+0.04% 🔺)
@sentry/browser - Webpack (gzipped)	22.44 KB (+0.17% 🔺)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	75.88 KB (-0.25% 🔽)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	67.44 KB (-0.23% 🔽)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	33.38 KB (+0.03% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped)	24.48 KB (+0.08% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	212.64 KB (-0.27% 🔽)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	101.19 KB (+0.16% 🔺)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	73.6 KB (+0.26% 🔺)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	36.62 KB (+0.23% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	69.49 KB (-0.28% 🔽)
@sentry/react - Webpack (gzipped)	22.47 KB (+0.07% 🔺)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	87.31 KB (-0.14% 🔽)
@sentry/nextjs Client - Webpack (gzipped)	50.42 KB (+0.13% 🔺)
@sentry-internal/feedback - Webpack (gzipped)	17.11 KB (-0.07% 🔽)

[Lms24]

Looking forward to deleting the hub counterpart

[mydea]

I've updated this to also fix/remove the custom handling for this in opentelemetry/node-experimental (which was the reason some tests failed etc.)