docs(logs): update nextjs logs implementation docs

[jonmcwest]

Changes

Improved the Next.js logs installation guide with better practices for handling log flushing in serverless environments:

1. Moved the LoggerProvider creation outside the register() function so it can be exported and used in route handlers
2. Added instructions for manually flushing logs using the after() function from next/server
3. Repositioned the note about Next.js 15+ instrumentation hook being enabled by default to appear before the code example
4. Added Next.js to the logs installation navigation menu

These changes ensure logs are properly sent before serverless functions freeze, which is critical for reliable logging in Next.js applications.

Checklist

• I've read the docs and/or content style guides.
• Words are spelled using American English
• Use relative URLs for internal links
• I've checked the pages added or changed in the Vercel preview build
• If I moved a page, I added a redirect in vercel.json

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Project	Deployment	Review	Updated (UTC)
posthog	Ready	Preview	Jan 28, 2026 9:18pm

[jonmcwest]

• docs(logs): update nextjs logs implementation docs #14616 👈 (View in Graphite)
• master

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[corywatilo]

Also missing nav link for Next.js

#14614 (comment)