feat(aws): Add support for streaming handlers

[msonnb]

blocked by open-telemetry/opentelemetry-js-contrib#2970

closes #15774

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	24.04 kB	-	-
@sentry/browser - with treeshaking flags	22.62 kB	-	-
@sentry/browser (incl. Tracing)	39.75 kB	-	-
@sentry/browser (incl. Tracing, Replay)	77.86 kB	-	-
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	67.69 kB	-	-
@sentry/browser (incl. Tracing, Replay with Canvas)	82.56 kB	-	-
@sentry/browser (incl. Tracing, Replay, Feedback)	94.66 kB	-	-
@sentry/browser (incl. Feedback)	40.7 kB	-	-
@sentry/browser (incl. sendFeedback)	28.7 kB	-	-
@sentry/browser (incl. FeedbackAsync)	33.59 kB	-	-
@sentry/react	25.76 kB	-	-
@sentry/react (incl. Tracing)	41.69 kB	-0.01%	-4 B 🔽
@sentry/vue	28.5 kB	-	-
@sentry/vue (incl. Tracing)	41.56 kB	-	-
@sentry/svelte	24.07 kB	-	-
CDN Bundle	25.55 kB	-	-
CDN Bundle (incl. Tracing)	39.64 kB	-	-
CDN Bundle (incl. Tracing, Replay)	75.7 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback)	81.11 kB	-	-
CDN Bundle - uncompressed	74.7 kB	-	-
CDN Bundle (incl. Tracing) - uncompressed	117.32 kB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	231.59 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	244.19 kB	-	-
@sentry/nextjs (client)	43.75 kB	-	-
@sentry/sveltekit (client)	40.2 kB	-	-
@sentry/node-core	47.73 kB	+0.01%	+1 B 🔺
@sentry/node	146.62 kB	+0.01%	+1 B 🔺
@sentry/node - without tracing	91.83 kB	-	-
@sentry/aws-serverless	103.31 kB	+0.04%	+41 B 🔺

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