feat(anthropic) add docs for anthropic integration

[constantinius]

DESCRIBE YOUR PR

Adds docs for the anthropic integration done with getsentry/sentry-python#4674

Part of https://linear.app/getsentry/issue/TET-996/improve-integration-for-anthropic-sdk

PRE-MERGE CHECKLIST

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• Checked Vercel preview for correctness, including links
• PR was reviewed and approved by any necessary SMEs (subject matter experts)
• PR was reviewed and approved by a member of the Sentry docs team

[linear]

TET-996 Improve integration for Anthropic SDK

[vercel]

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Project	Deployment	Preview	Comments	Updated (UTC)
sentry-docs	✅ Ready	Preview	Comment	Aug 14, 2025 4:45pm

1 Skipped Deployment

Project	Deployment	Preview	Comments	Updated (UTC)
develop-docs	⬜️ Ignored	Preview		Aug 14, 2025 4:45pm

[codecov]

Bundle Report

Changes will increase total bundle size by 3.35kB (0.01%) ⬆️. This is within the configured threshold ✅

Detailed changes

Bundle name	Size	Change
sentry-docs-client-array-push	9.85MB	-6 bytes (-0.0%) ⬇️
sentry-docs-server-cjs	12.37MB	3.36kB (0.03%) ⬆️

Affected Assets, Files, and Routes:

view changes for bundle: sentry-docs-server-cjs

Assets Changed:

Asset Name	Size Change	Total Size	Change (%)
1729.js	-3 bytes	1.77MB	-0.0%
../instrumentation.js	-3 bytes	1.1MB	-0.0%
9523.js	-3 bytes	1.08MB	-0.0%
../app/[[...path]]/page.js.nft.json	1.12kB	743.85kB	0.15%
../app/platform-redirect/page.js.nft.json	1.12kB	743.76kB	0.15%
../app/sitemap.xml/route.js.nft.json	1.12kB	741.23kB	0.15%

view changes for bundle: sentry-docs-client-array-push

Assets Changed:

Asset Name	Size Change	Total Size	Change (%)
static/chunks/pages/_app-*.js	-3 bytes	882.71kB	-0.0%
static/chunks/8321-*.js	-3 bytes	425.87kB	-0.0%
static/1Usq1-*.js (New)	684 bytes	684 bytes	100.0% 🚀
static/1Usq1-*.js (New)	77 bytes	77 bytes	100.0% 🚀
static/cE9kb5NNoWm88O49pij6k/_buildManifest.js (Deleted)	-684 bytes	0 bytes	-100.0% 🗑️
static/cE9kb5NNoWm88O49pij6k/_ssgManifest.js (Deleted)	-77 bytes	0 bytes	-100.0% 🗑️

[antonpirker]

Looks great!

[coolguyzone]

Is this list going to grow? If not, I would consider reformatting from a list to something like "include_prompts is the only keyword argument you can pass into AnthropicIntegration()."

[coolguyzone]

Thanks for adding!