error TypeError: Cannot read properties of undefined (reading '') when using Next.js runtime edge on turborepo or Nx

Verify canary release

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

Provide environment information

Operating System:
      Platform: win32
      Arch: x64
      Version: Windows 10 Pro   
    Binaries:
      Node: 18.16.0
      npm: N/A
      Yarn: N/A
      pnpm: N/A
    Relevant Packages:
      next: 13.4.13-canary.13   
      eslint-config-next: 13.4.1
      react: 18.2.0
      react-dom: 18.2.0
      typescript: 4.9.5
    Next.js Config:
      output: N/A

Which area(s) of Next.js are affected? (leave empty if unsure)

App Router, Middleware / Edge (API routes, runtime)

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

https://github.com/NastykSwED/turbo-next-edge

To Reproduce

1. Run pnpm install to install the dependencies.
2. Run pnpm dev to get both projects up or run pnpm dev --filter [docs | web].
3. Go to http://localhost:3001/ or http://localhost:3000/ and see the console for the following error:
   

And in the browser:

Describe the Bug

When using the runtime edge on a monorepo such as turborepo or Nx, the console throws the error: "- error TypeError: Cannot read properties of undefined (reading '')". This only happens with monorepos, when using standalone applications this does not happen.

Expected Behavior

It should not throw the above error when using a Nextjs app with the runtime edge on a monorepo.

Which browser are you using? (if relevant)

Microsoft Edge Versión 115.0.1901.188 (Compilación oficial) (64 bits)

How are you deploying your application? (if relevant)

No response

_NEXT-1513

Start with the linked turbo-next-edge reproduction and run pnpm install followed by pnpm dev, or pnpm dev --filter docs or web. Compare the monorepo behavior with a standalone Next.js app using the edge runtime, focusing on the App Router and Middleware / Edge areas named in the report. Done means the reproduced applications start without the undefined-property error in the console or browser.