Hi!
Noticed that if one sets a cookie value in middleware then it is not updated in the same request further down in pages and server component.
Tried to make a minimal repro with the following:
middleware.js:

import { NextResponse } from 'next/server';

export function middleware(request) {
  console.log('--------');
  console.log('initial', request.cookies.get('test')?.value);

  const value = new Date().valueOf();
  console.log('middleware', value);
  request.cookies.set('test', value);

  const response = NextResponse.next();
  response.cookies.set('test', value);

  return response;
}

export const config = {
  matcher: ['/((?!api|_next/static|_next/image|favicon.ico).*)'],
};

root page.jsx:

import { cookies } from 'next/headers';

export default function () {
  const value = cookies().get('test')?.value;
  console.log('page', value);

  return <div />;
}

Logs I am getting refreshing the page 2 times

initial 1698448854995
middleware 1698448860030
page 1698448854995
--------
initial 1698448860030
middleware 1698448862946
page 1698448860030

You can see initial cookies().get() and in the page values basically lag 1 page update behind

Am I missing something here? Is it possible to set a cookie value in middleware and read it in the same request in server components? Thanks!