fix(node): Fix vercel flushing logic & add test for it

[mydea]

As pre-work for #16178, actually add a test for this (kind of). This showed that there was actually a fundamental flaw here, as we looked as the req not the res, oops.

[github-actions]

size-limit report 📦

⚠️ Warning: Base artifact is not the latest one, because the latest workflow run is not done yet. This may lead to incorrect results. Try to re-run all tests to get up to date results.

Path	Size	% Change	Change
@sentry/browser	23.34 KB	-	-
@sentry/browser - with treeshaking flags	23.16 KB	-	-
@sentry/browser (incl. Tracing)	37.22 KB	-	-
@sentry/browser (incl. Tracing, Replay)	74.45 KB	-	-
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	68.32 KB	-	-
@sentry/browser (incl. Tracing, Replay with Canvas)	79.11 KB	-	-
@sentry/browser (incl. Tracing, Replay, Feedback)	90.93 KB	-	-
@sentry/browser (incl. Feedback)	39.72 KB	-	-
@sentry/browser (incl. sendFeedback)	27.96 KB	-	-
@sentry/browser (incl. FeedbackAsync)	32.72 KB	-	-
@sentry/react	25.14 KB	-	-
@sentry/react (incl. Tracing)	39.22 KB	-	-
@sentry/vue	27.6 KB	-	-
@sentry/vue (incl. Tracing)	38.99 KB	-	-
@sentry/svelte	23.36 KB	-	-
CDN Bundle	24.55 KB	-	-
CDN Bundle (incl. Tracing)	37.3 KB	-	-
CDN Bundle (incl. Tracing, Replay)	72.34 KB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback)	77.62 KB	-	-
CDN Bundle - uncompressed	71.62 KB	-	-
CDN Bundle (incl. Tracing) - uncompressed	110.34 KB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	221.63 KB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	234.15 KB	-	-
@sentry/nextjs (client)	40.83 KB	-	-
@sentry/sveltekit (client)	37.72 KB	-	-
@sentry/node	144.31 KB	+0.04%	+53 B 🔺
@sentry/node - without tracing	96.19 KB	+0.06%	+56 B 🔺
@sentry/aws-serverless	120.56 KB	+0.05%	+60 B 🔺

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