NextCustomServer overwrites req.url with internal NextJS path

Link to the code that reproduces this issue or a replay of the bug

https://github.com/tills13/nextjs-req-url-reproduction

To Reproduce

1. install deps (npm ci)
2. build next (npx next build)
3. run server (node server.js)
4. navigate to http://localhost:3000 (any path)
5. note that the URL is the internal NextJS URL instead of the expected user-facing URL

Current vs. Expected behavior

The expected behaviour is that, for Custom Servers, at least, the request URL is untouched as you might want to render a page at a different path than what the URL path is e.g. /blog/some-slug/ -> /pages/blog_post.js

Our sites do not have uniform URLs (both /blog/some-slug/ and /some-slug/ might refer to a blog post or a static page and we don't know until we resolve the object from our CMS) so we cannot use file system routing.

Verify canary release

• I verified that the issue exists in the latest Next.js canary release

Provide environment information

Operating System:
      Platform: linux
      Arch: x64
      Version: #1 SMP Fri Jan 27 02:56:13 UTC 2023
    Binaries:
      Node: 16.20.0
      npm: 8.19.4
      Yarn: N/A
      pnpm: N/A
    Relevant Packages:
      next: 13.4.20-canary.27
      eslint-config-next: N/A
      react: 18.2.0
      react-dom: 18.2.0
      typescript: N/A
    Next.js Config:
      output: N/A

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

Routing (next/router, next/navigation, next/link)

Additional context

Seems like the issue was introduce in https://github.com/vercel/next.js/pull/49805 or https://github.com/vercel/next.js/pull/53523

Use the linked reproduction repository and follow its npm ci, npx next build, and node server.js steps. Start with server.js and the custom-server request path, then verify that navigating to any path leaves req.url as the user-facing URL rather than an internal Next.js path.