Expose api to communicate with Studio `app`

[maximepvrt]

It would be helpful if useStudio() (or an equivalent API) were exposed so developers can detect whether the Nuxt Studio menu is open, open the menu, …. This would allow layouts and components to reactively adapt to the Studio sidebar state.

[larbish]

We'll work on this to improve the Docus experience (ie, click on "edit this page" can open the related page in Studio).

As a temporary workaround, you can use location info from local storage: https://github.com/nuxt-content/studio/blob/main/src/app/src/composables/useStudioState.ts#L10