docs(js): Differentiate manual and automatic AI instrumentation - #16843

DESCRIBE YOUR PR

Updates the AI integration setup docs to have a distinction between automatic and manual setup (previously called "server-side" and "browser-side").

There are several other runtimes (other than Browser) where automatic instrumentation does not work.

Automatic setup only works in Node runtimes, so the two sections are shown as follows:

• Automatic: Node-based SDKs ([Current] [PR Preview])
• Automatic and Manual: Meta-Frameworks, Hono, and Serverless SDKs ([Current] [PR Preview])
• Manual: Cloudflare, Bun ([Current] [PR Preview]) and Browser-side only SDKs ([Current] [PR Preview])

Reference issue: getsentry/sentry-javascript#19696

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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