ref(core): Add more specific exception mechanism for internal errors

[Lms24]

see #17212
part of #17252

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	23.77 kB	+0.02%	+4 B 🔺
@sentry/browser - with treeshaking flags	22.36 kB	+0.05%	+11 B 🔺
@sentry/browser (incl. Tracing)	39.42 kB	+0.03%	+10 B 🔺
@sentry/browser (incl. Tracing, Replay)	77.55 kB	+0.02%	+14 B 🔺
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	67.41 kB	+0.02%	+11 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	82.25 kB	+0.02%	+12 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback)	94.37 kB	+0.01%	+5 B 🔺
@sentry/browser (incl. Feedback)	40.46 kB	+0.01%	+4 B 🔺
@sentry/browser (incl. sendFeedback)	28.45 kB	+0.03%	+7 B 🔺
@sentry/browser (incl. FeedbackAsync)	33.35 kB	+0.02%	+6 B 🔺
@sentry/react	25.51 kB	+0.04%	+8 B 🔺
@sentry/react (incl. Tracing)	41.39 kB	+0.01%	+2 B 🔺
@sentry/vue	28.2 kB	+0.02%	+5 B 🔺
@sentry/vue (incl. Tracing)	41.22 kB	+0.02%	+5 B 🔺
@sentry/svelte	23.8 kB	+0.03%	+6 B 🔺
CDN Bundle	25.29 kB	+0.03%	+7 B 🔺
CDN Bundle (incl. Tracing)	39.3 kB	+0.04%	+14 B 🔺
CDN Bundle (incl. Tracing, Replay)	75.42 kB	+0.02%	+15 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback)	80.85 kB	+0.02%	+15 B 🔺
CDN Bundle - uncompressed	73.9 kB	+0.06%	+39 B 🔺
CDN Bundle (incl. Tracing) - uncompressed	116.34 kB	+0.04%	+39 B 🔺
CDN Bundle (incl. Tracing, Replay) - uncompressed	230.65 kB	+0.02%	+39 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	243.46 kB	+0.02%	+39 B 🔺
@sentry/nextjs (client)	43.44 kB	+0.02%	+5 B 🔺
@sentry/sveltekit (client)	39.85 kB	+0.02%	+6 B 🔺
@sentry/node-core	47.53 kB	+0.02%	+7 B 🔺
@sentry/node	145.86 kB	+0.01%	+7 B 🔺
@sentry/node - without tracing	91.64 kB	+0.01%	+7 B 🔺
@sentry/aws-serverless	103.09 kB	+0.01%	+8 B 🔺

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