// if there is no posts return 404 with custom message
if( empty($query->posts) ){
    return new WP_Error( 'no_posts', __('No post found'), array( 'status' => 404 ) ); // status can be changed to any number
}

// output
{
    "code": "no_posts",
    "message": "No post found",
    "data": {
        "status": 404
    }
}