recursion_transform_tree.php

<?php
function transform_tree($categories) {
    $data = [];

    foreach($categories as $key => $category) {
        $data[$key] = [
            'name' = $category->name
        ];

        if ($category->children) {
            $data[$key]['children'] = transform_tree($category->children);
        }

        if ($category->audio) {
            $data[$key]['downloadable'] = true;
            $data[$key]['audio'] = $category->audio;
        }
    }

    return $data;
}

// build

$trees = build_tree($categories);