feat(core): Improve error handling for Anthropic AI instrumentation

[RulaKhaled]

This PR enhances Anthropic AI instrumentation to properly handle and record errors that occur as part of response metadata.

Core Error Handling Improvements:

• Enhanced error detection: Added proper handling for Anthropic API error responses with type: 'error' structure
• Improved streaming error handling: Better error type detection and reporting for streaming operations
• Error capturing: Manually captured errors for both standard and streaming errors

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	24.17 kB	-	-
@sentry/browser - with treeshaking flags	22.75 kB	-	-
@sentry/browser (incl. Tracing)	40.14 kB	-	-
@sentry/browser (incl. Tracing, Replay)	78.5 kB	-	-
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	68.26 kB	-	-
@sentry/browser (incl. Tracing, Replay with Canvas)	83.18 kB	-	-
@sentry/browser (incl. Tracing, Replay, Feedback)	95.38 kB	-	-
@sentry/browser (incl. Feedback)	40.91 kB	-	-
@sentry/browser (incl. sendFeedback)	28.82 kB	-	-
@sentry/browser (incl. FeedbackAsync)	33.77 kB	-	-
@sentry/react	25.89 kB	-	-
@sentry/react (incl. Tracing)	42.11 kB	-	-
@sentry/vue	28.66 kB	-	-
@sentry/vue (incl. Tracing)	41.95 kB	-	-
@sentry/svelte	24.2 kB	-	-
CDN Bundle	25.76 kB	-	-
CDN Bundle (incl. Tracing)	40.01 kB	-	-
CDN Bundle (incl. Tracing, Replay)	76.29 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback)	81.75 kB	-	-
CDN Bundle - uncompressed	75.2 kB	-	-
CDN Bundle (incl. Tracing) - uncompressed	118.31 kB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	233.4 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	246.16 kB	-	-
@sentry/nextjs (client)	44.14 kB	-	-
@sentry/sveltekit (client)	40.58 kB	-	-
@sentry/node-core	49.66 kB	-	-
@sentry/node	150.7 kB	+0.03%	+45 B 🔺
@sentry/node - without tracing	92.23 kB	-	-
@sentry/aws-serverless	105.53 kB	-	-

View base workflow run

[github-actions]

node-overhead report 🧳

Note: This is a synthetic benchmark with a minimal express app and does not necessarily reflect the real-world performance impact in an application.

Scenario	Requests/s	% of Baseline	Prev. Requests/s	Change %
GET Baseline	9,084	-	8,832	+3%
GET With Sentry	1,368	15%	1,325	+3%
GET With Sentry (error only)	5,986	66%	5,846	+2%
POST Baseline	1,209	-	1,193	+1%
POST With Sentry	496	41%	477	+4%
POST With Sentry (error only)	1,069	88%	1,055	+1%
MYSQL Baseline	3,357	-	3,306	+2%
MYSQL With Sentry	461	14%	435	+6%
MYSQL With Sentry (error only)	2,710	81%	2,702	+0%

View base workflow run

[Lms24]

Thanks a lot for setting the mechanism. I had two remarks but as I wrote, might be missing some context.