HMR doesn't work behind Firebase Hosting from version 13.4.3

[dobrac]

Verify canary release

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

Provide environment information

Operating System:
      Platform: darwin
      Arch: arm64
      Version: Darwin Kernel Version 22.5.0: Mon Apr 24 20:52:24 PDT 2023; root:xnu-8796.121.2~5/RELEASE_ARM64_T6000
    Binaries:
      Node: 18.16.0
      npm: 9.5.1
      Yarn: 1.22.19
      pnpm: 8.5.1
    Relevant packages:
      next: 13.4.4-canary.6
      eslint-config-next: 13.4.3
      react: 18.2.0
      react-dom: 18.2.0
      typescript: 5.0.4

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

No response

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

https://github.com/dobrac/nextjs-firebase-hmr-bug

To Reproduce

(The bug reproduction is on v13.4.4-canary.6, because v13.4.4-canary.7 is broken and doesn't start)

1. yarn install
2. firebase experiments:enable webframeworks
3. yarn devFirebaseEmulators
4. Change index.tsx in the "pages" folder or page.tsx in the "app/app" folder
5. Observe change in the browser

Describe the Bug

Both pages (in "pages" or "app") are not refreshed, making HMR not working. In devtools, hmr websocket is never connected to the server.

This happens only if "app" directory exists, it's not dependent on the "pages" directory. Also running the application without Firebase hosting, HMR works.

This bug was is not present in NextJS version v13.4.2.

Expected Behavior

HMR works and websocket connects correctly.

Which browser are you using? (if relevant)

Arc 0.104.0 (38955)

How are you deploying your application? (if relevant)

Firebase Hosting, but running emulator locally

[dobrac]

These issues seem to be related #50461, #50400