Response cookies missing in middleware

Link to the code that reproduces this issue

https://github.com/marcospassos/next-middleware-cookie-bug

To Reproduce

If you set a cookie in a server action, it is not available in the middleware. Without this, the middleware cannot prevent overriding cookies that may be set at the request time.

To Reproduce

Create a server action:

'use server';

import {cookies} from 'next/headers';

export async function example(): Promise<void> {
    cookies().set('foo', 'bar');
}

Then, in your middleware:

export function middleware(): void {
    const response = NextResponse.next();
    
    console.log(response.cookies.has('foo'));   
}

The result is always false.

Current vs. Expected behavior

The response should include the cookies set in server actions.

Provide environment information

Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 23.4.0: Fri Mar 15 00:12:25 PDT 2024; root:xnu-10063.101.17~1/RELEASE_ARM64_T6030
  Available memory (MB): 18432
  Available CPU cores: 11
Binaries:
  Node: 21.7.3
  npm: 10.5.0
  Yarn: N/A
  pnpm: N/A
Relevant Packages:
  next: 14.2.3 // Latest available version is detected (14.2.3).
  eslint-config-next: 14.0.3
  react: 18.3.1
  react-dom: 18.3.1
  typescript: 5.4.5
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)

Additional context

No response