Changing locale causes all components to be in Unmounted state

[martinszeltins]

Environment

------------------------------
- Operating System: Linux
- Node Version:     v20.11.0
- Nuxt Version:     3.11.2
- CLI Version:      3.11.1
- Nitro Version:    2.9.6
- Package Manager:  npm@10.2.4
- Builder:          -
- User Config:      modules, i18n
- Runtime Modules:  @nuxtjs/i18n@8.3.1
- Build Modules:    -
------------------------------

Reproduction

https://stackblitz.com/github/martinszeltins/nuxt-i18n-unmounted

Describe the bug

When using setLocale() to change locale, it causes all of the components to be left in an Unmounted state.

Please see the reproduction. When you click the Change Locale button, which uses setLocale to change the locale, we see this output in console:

onMounted
onMounted
onUnmounted
onUnmounted

The last lifecycle hook that triggered was the onUnmounted hook. Now all components think that they are unmounted when actually they are not unmounted.

This causes all kinds of issues because usually in onUnmounted hook we perform cleanup, remove event listeners etc. and it causes the app to break.

Screenshot:

Additional context

No response

Logs

No response