docs(js): Add browser AI integrations to SDK tables

[nabi-noor]

DESCRIBE YOUR PR

Adds Anthropic, Google Gen AI, LangChain, LangGraph, and OpenAI to the browser integration tables for Astro, Gatsby, Next.js, Nuxt, Remix, SolidStart, SvelteKit, and Vue.

These SDK-specific tables override the generic JavaScript table, so they did not inherit the browser AI integration entries added in #15736. The new rows link to the existing Agent Tracing guides and identify these integrations as opt-in tracing and additional-context integrations in browser runtimes.

Fixes getsentry/sentry-javascript#18799

AI assistance disclosure: OpenAI Codex assisted with repository inspection, implementation, and validation. The commit includes the corresponding co-author attribution.

IS YOUR CHANGE URGENT?

Help us prioritize incoming PRs by letting us know when the change needs to go live.
Select exactly one option. For deadlines, replace YYYY-MM-DD with the due date. You can update this information later by editing the PR description.

• Urgent deadline (GA date, etc.): YYYY-MM-DD
• Other deadline: YYYY-MM-DD
• No deadline: Not urgent, can wait up to 1 week+

SLA

• Teamwork makes the dream work, so please add a reviewer to your PRs.
• Please give the docs team up to 1 week to review your PR unless you've supplied a deadline.

Thanks in advance for your help!

PRE-MERGE CHECKLIST

Make sure you've checked the following before merging your changes:

• 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

LEGAL BOILERPLATE

Look, I get it. The entity doing business as "Sentry" was incorporated in the State of Delaware in 2015 as Functional Software, Inc. and is gonna need some rights from me in order to utilize my contributions in this here PR. So here's the deal: I retain all rights, title and interest in and to my contributions, and by keeping this boilerplate intact I confirm that Sentry can use, modify, copy, and redistribute my contributions, under Sentry's choice of terms.

EXTRA RESOURCES

• Sentry Docs contributor guide

[vercel]

@nabi-noor is attempting to deploy a commit to the Sentry Team on Vercel.

A member of the Team first needs to authorize it.

[nabi-noor]

@getsentry/docs, could you please review this contribution when available? The external-fork Vercel previews currently require authorization from a Sentry team member; the full production build and test suite pass locally.