ref(core): Avoid looking up anthropic-ai integration options

[mydea]

This avoids looking up the integration for anthropic-ai instrumentation, instead relying on this being passed in (which it already is). When manually instrumenting the client you need to pass in the options directly.

1. Node: Options are passed from the integration to instrumentAnthropicAiClient anyhow, so nothing changes
2. cloudflare/vercel-edge: There is no integration, users need to manually call instrumentAnthropicAiClient() and pass in the options anyhow (no integration to look anything up from exists there)

This required updating the tests to actually use auto instrumentation properly instead of manual client wrapping, which is overall a good change anyhow IMHO.

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	24.22 kB	-	-
@sentry/browser - with treeshaking flags	22.74 kB	-	-
@sentry/browser (incl. Tracing)	40.23 kB	-	-
@sentry/browser (incl. Tracing, Replay)	78.6 kB	-	-
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	68.27 kB	-	-
@sentry/browser (incl. Tracing, Replay with Canvas)	83.26 kB	-	-
@sentry/browser (incl. Tracing, Replay, Feedback)	95.49 kB	-	-
@sentry/browser (incl. Feedback)	40.94 kB	-	-
@sentry/browser (incl. sendFeedback)	28.88 kB	-	-
@sentry/browser (incl. FeedbackAsync)	33.78 kB	-	-
@sentry/react	25.93 kB	-	-
@sentry/react (incl. Tracing)	42.23 kB	-	-
@sentry/vue	28.71 kB	-	-
@sentry/vue (incl. Tracing)	42.04 kB	-	-
@sentry/svelte	24.24 kB	-	-
CDN Bundle	25.75 kB	-	-
CDN Bundle (incl. Tracing)	40.05 kB	-	-
CDN Bundle (incl. Tracing, Replay)	76.28 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback)	81.78 kB	-	-
CDN Bundle - uncompressed	75.23 kB	-	-
CDN Bundle (incl. Tracing) - uncompressed	118.58 kB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	233.71 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	246.47 kB	-	-
@sentry/nextjs (client)	44.23 kB	-	-
@sentry/sveltekit (client)	40.66 kB	-	-
@sentry/node-core	49.96 kB	-0.01%	-1 B 🔽
@sentry/node	151.18 kB	-0.05%	-73 B 🔽
@sentry/node - without tracing	91.86 kB	-0.01%	-1 B 🔽
@sentry/aws-serverless	105.31 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	9,114	-	9,262	-2%
GET With Sentry	1,432	16%	1,394	+3%
GET With Sentry (error only)	6,102	67%	5,999	+2%
POST Baseline	1,213	-	1,179	+3%
POST With Sentry	561	46%	560	+0%
POST With Sentry (error only)	1,077	89%	1,061	+2%
MYSQL Baseline	3,358	-	3,310	+1%
MYSQL With Sentry	504	15%	421	+20%
MYSQL With Sentry (error only)	2,749	82%	2,677	+3%

View base workflow run

[RulaKhaled]

lgtm