how to use spatie permission in vue 3 with laravel backend

Spatie permission package is only working on back-end and not related to front-end. So you need to pass that information yourself.

That's how I do it, image we have a post API resource

return [
	'id' => '...',
	'title' => '...',
	'content' => '...',
	'can' => [
		'edit' => auth()->user()->can('edit posts'),
		'delete' => auth()->user()->can('delete posts')
	]
];

That's an example of Laracasts response