fix: Fork scope and keep async context within startSpan and startSpanManual

[lforst]

In order to make sure spans are correctly nested when startSpan and startSpanManual are called we need to fork the scope and keep track of the async context in their callbacks.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	78.18 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	69.39 KB (+0.02% 🔺)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	73.28 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	63.01 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	33.41 KB (+0.03% 🔺)
@sentry/browser (incl. browserTracingIntegration) - Webpack (gzipped)	33.27 KB (+0.03% 🔺)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.33 KB (0%)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.34 KB (0%)
@sentry/browser - Webpack (gzipped)	22.6 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	76 KB (+0.05% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	67.54 KB (+0.04% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	33.45 KB (+0.13% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped)	24.66 KB (+0.14% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	213.12 KB (+0.07% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	101.13 KB (+0.14% 🔺)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	74 KB (+0.16% 🔺)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	36.56 KB (+0.11% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	69.78 KB (-0.02% 🔽)
@sentry/react - Webpack (gzipped)	22.63 KB (0%)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	86.45 KB (+0.01% 🔺)
@sentry/nextjs Client - Webpack (gzipped)	50.76 KB (+0.01% 🔺)
@sentry-internal/feedback - Webpack (gzipped)	17.21 KB (0%)