NextResponse.rewrite does not override origin server headers

Link to the code that reproduces this issue

https://github.com/Gebov/nextjs-rewrite-headers

To Reproduce

1. Start the app
2. Request /rewrite
3. Inspect the response headers
4. Verify that the Cache-Control header is not overriden
5. Verify that the custom header is overriden

Current vs. Expected behavior

Currently the app is configured to proxy requests to nextjs.org with the URL /rewrite.

I expect all the headers specified in the NextResponse.headers to be overriden. In particular the Cache-Control header.
Currently it is not overriden. Custom headers work.

Provide environment information

Operating System:
  Platform: win32
  Arch: x64
  Version: Windows 11 Enterprise
  Available memory (MB): 32488
  Available CPU cores: 16
Binaries:
  Node: 20.15.0
  npm: N/A
  Yarn: N/A
  pnpm: N/A
Relevant Packages:
  next: 14.2.13 // Latest available version is detected (14.2.13).
  eslint-config-next: N/A
  react: 18.3.1
  react-dom: 18.3.1
  typescript: N/A
Next.js Config:
  output: N/A

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

Middleware

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

next dev (local), next start (local)

Additional context

No response

Start with the linked reproduction repository and follow its /rewrite request in next dev and next start. Inspect the middleware response headers, especially NextResponse.headers and the proxied origin response. Done means the specified Cache-Control header and custom headers both override the origin headers.