Pages Router does not use updated cookies from Proxy `response.cookies.set()`, unlike App Router

Link to the code that reproduces this issue

https://github.com/thomasboyt/nextjs-broken-pages-router-proxy-cookies-behavior

To Reproduce

1. next dev
2. Visit localhost:3000/app-demo. Notice that the new cookie value is displayed correctly in the rendered component.
3. Clear your cookies.
4. Visit localhost:3000/pages-demo. Notice that the new cookie value is not displayed correctly.
5. Refresh. Notice the new cookie value is now displayed correctly.

Current vs. Expected behavior

The Pages Router should support the same behavior as App Router, as implemented in https://github.com/vercel/next.js/pull/65008: setting cookies using response.cookies.set() should show the new cookie values in ctx.req.cookies in getServerSideProps, as they show up in next/headers's cookies() function in App Router.

Otherwise, the documentation on https://nextjs.org/docs/pages/api-reference/file-conventions/proxy#using-cookies should be updated to indicate this is expected to not work in Pages Router.

Provide environment information

Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 25.3.0: Wed Jan 28 20:48:41 PST 2026; root:xnu-12377.81.4~5/RELEASE_ARM64_T6041
  Available memory (MB): 49152
  Available CPU cores: 16
Binaries:
  Node: 22.22.0
  npm: 10.9.4
  Yarn: N/A
  pnpm: N/A
Relevant Packages:
  next: 16.2.0-canary.51 // Latest available version is detected (16.2.0-canary.51).
  eslint-config-next: N/A
  react: 19.2.3
  react-dom: 19.2.3
  typescript: 5.9.3
Next.js Config:
  output: N/A

Which area(s) are affected? (Select all that apply)

Pages Router, Middleware

Which stage(s) are affected? (Select all that apply)

next dev (local), next start (local)

Additional context

This is blocking an incremental rewrite of my application in App Router. My application heavily used getServerSideProps and set various cookies in its logic. I am trying to move the logic that was used for all requests to proxy.ts, as App Router does not allow setting cookies during server-side rendering. Unfortunately, right now I cannot rely on proxy.ts cookie setting to work correctly in Pages Router.

I may have to implement a manual workaround using headers added to the request.

Run the linked reproduction with both /app-demo and /pages-demo, then compare the Proxy response.cookies.set() path with getServerSideProps and ctx.req.cookies in the Pages Router. Check the related App Router behavior from PR 65008. Done means updated cookie values are available in Pages Router requests, or the Pages Router cookie limitation is documented at the cited Proxy documentation page.