fix: Component tree not loading in popup

[TechAkayy]

🐛 The bug

Component tree loads just fine when it's in-app, and doesn't load in the popup picture-in-picture mode, probably losing connection with the app.

Popup doesn't work in stackblitz due to a limitation explained in this issue #687, so below reproduction is a github for cloning and testing it in local dev environment.

In-app:

Popup:

• Browser - Chrome Version 126.0.6478.114 (Official Build) (arm64)
• Operating System: Darwin
• Node Version: v20.14.0
• Nuxt Version: 3.12.3
• CLI Version: 3.12.0
• Nitro Version: 2.9.7
• Package Manager: npm@10.7.0
• Builder: -
• User Config: devtools, modules
• Runtime Modules: -
• Build Modules: -

🛠️ To reproduce

https://github.com/TechAkayy/nuxt-devtools-popup

🌈 Expected behavior

Popup should connect to the app and load component tree.

ℹ️ Additional context

No response

[fmoessle]

It also doesn't work with Pinia. using the lastest version of nuxt and devtools.