After() docs requests API (#89837)
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### What?
Reworded the "With request APIs" section in the `after()` documentation.
### Why?
To clearly differentiate when `cookies()` and `headers()` can be used
inside `after()` in App Router pages (Server Components) versus Route
Handlers/Server Functions, addressing potential confusion and potential
runtime errors.
### How?
- Split the "With request APIs" section into two subsections: "In Route
Handlers and Server Functions" and "In Server Components (pages and
layouts)".
- Clarified that `cookies()`/`headers()` can be used directly in
`after()` for Route Handlers/Server Functions.
- Explained that `cookies()`/`headers()` *cannot* be used directly in
`after()` for Server Components due to partial prerendering/Cache
Components, and will throw a runtime error.
- Added a new code example demonstrating the correct pattern for Server
Components (reading request data *before* `after()` and passing it in).
- Corrected `await` syntax in existing Route Handler examples and
updated highlight line numbers.
Closes NEXT-
Fixes #
-->
---
[Slack
Thread](https://vercel.slack.com/archives/C03KAR5DCKC/p1770819029314169?thread_ts=1770819029.314169&cid=C03KAR5DCKC)
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Co-authored-by: Cursor Agent <cursoragent@cursor.com>
Co-authored-by: Joseph Chamochumbi <joseph.chamochumbi@vercel.com>
