feat(replay): Expose recordingMode in public API

[chargome]

closes #13987

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	22.73 KB	-	-
@sentry/browser - with treeshaking flags	21.52 KB	-	-
@sentry/browser (incl. Tracing)	35.11 KB	-	-
@sentry/browser (incl. Tracing, Replay)	71.82 KB	+0.05%	+32 B 🔺
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	62.26 KB	+0.02%	+10 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	76.13 KB	+0.02%	+11 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback)	88.94 KB	+0.01%	+7 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback, metrics)	90.77 KB	+0.01%	+9 B 🔺
@sentry/browser (incl. metrics)	26.98 KB	-	-
@sentry/browser (incl. Feedback)	39.87 KB	-	-
@sentry/browser (incl. sendFeedback)	27.37 KB	-	-
@sentry/browser (incl. FeedbackAsync)	32.17 KB	-	-
@sentry/react	25.48 KB	-	-
@sentry/react (incl. Tracing)	38.07 KB	-	-
@sentry/vue	26.87 KB	-	-
@sentry/vue (incl. Tracing)	36.99 KB	-	-
@sentry/svelte	22.86 KB	-	-
CDN Bundle	24.08 KB	-	-
CDN Bundle (incl. Tracing)	36.92 KB	-	-
CDN Bundle (incl. Tracing, Replay)	71.58 KB	+0.02%	+10 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback)	76.92 KB	+0.02%	+12 B 🔺
CDN Bundle - uncompressed	70.62 KB	-	-
CDN Bundle (incl. Tracing) - uncompressed	109.61 KB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	222.13 KB	+0.05%	+95 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	235.35 KB	+0.04%	+95 B 🔺
@sentry/nextjs (client)	38.15 KB	-	-
@sentry/sveltekit (client)	35.71 KB	-	-
@sentry/node	129.6 KB	-	-
@sentry/node - without tracing	94.3 KB	+0.01%	+1 B 🔺
@sentry/aws-serverless	105.17 KB	-	-

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