fix: Export session API

[lforst]

Backport of #10711

Fixes #10696

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay, Feedback) - Webpack (gzipped)	78.42 KB (0%)
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	69.65 KB (0%)
@sentry/browser (incl. Tracing, Replay with Canvas) - Webpack (gzipped)	73.58 KB (0%)
@sentry/browser (incl. Tracing, Replay) - Webpack with treeshaking flags (gzipped)	63.26 KB (0%)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	33.6 KB (0%)
@sentry/browser (incl. browserTracingIntegration) - Webpack (gzipped)	33.48 KB (0%)
@sentry/browser (incl. Feedback) - Webpack (gzipped)	31.37 KB (0%)
@sentry/browser (incl. sendFeedback) - Webpack (gzipped)	31.38 KB (0%)
@sentry/browser - Webpack (gzipped)	22.64 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback) - ES6 CDN Bundle (gzipped)	76.71 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	68.2 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	34.02 KB (+0.05% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped)	25.01 KB (+0.07% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	214.85 KB (+0.03% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	102.65 KB (+0.06% 🔺)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	74.94 KB (+0.08% 🔺)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	37.16 KB (+0.05% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	70.01 KB (0%)
@sentry/react - Webpack (gzipped)	22.67 KB (0%)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	87.68 KB (0%)
@sentry/nextjs Client - Webpack (gzipped)	51.87 KB (0%)
@sentry-internal/feedback - Webpack (gzipped)	17.22 KB (0%)