Your Vue layout cannot dictate which layout it will be rendered in, because that's simply not accomplishable. However, there are other ways to solve what you want to do.
The most common way is to override the rootView method in app/Http/Middleware/HandleInertiaRequests
public function rootView(Request $request) {
if (/* Current request is front-end */) {
return 'frontend';
}
return parent::rootView($request);
}
How you determine that a request is front-end is up to you because I don't know your structure.