How can I make it so that the content of child categories is displayed when navigating through the parent element?

Question

Yii

Hello everybody! Tell me how to make it so that when you click on the parent element, get the output of all the materials of the child categories? The code below is not written by me, but I use it to display the category menu, this code is written as a widget.

public $tpl;
    public $model;
    public $data;
    public $tree;
    public $menuHtml;

    public function init(){
        parent::init();
        if( $this->tpl === null ){
            $this->tpl = 'menu';
        }
        $this->tpl .= '.php';
    }

    public function run(){
        if($this->tpl == 'menu.php'){
            $menu = Yii::$app->cache->get('menu');
            if($menu) return $menu;
        }

        $this->data = Category::find()->indexBy('id')->orderBy('position')->asArray()->all();
        $this->tree = $this->getTree();
        $this->menuHtml = $this->getMenuHtml($this->tree);
        
        if($this->tpl == 'menu.php'){
            set cache
            Yii::$app->cache->set('menu', $this->menuHtml, 60);
        }

        return $this->menuHtml;
    }

    protected function getTree(){
        $tree = [];
        foreach ($this->data as $id=>&$node) {
            if (!$node['parent_id'])
                $tree[$id] = &$node;
            else
                $this->data[$node['parent_id']]['childs'][$node['id']] = &$node;
        }
        return $tree;
    }

    protected function getMenuHtml($tree, $tab = ''){
        $str = '';
        foreach ($tree as $category) {
            $str .= $this->catToTemplate($category, $tab);
        }
        return $str;
    }

    protected function catToTemplate($category, $tab){
        ob_start();
        include __DIR__ . '/menu_tpl/' . $this->tpl;
        return ob_get_clean();
    }

The file responsible for displaying the category menu

<li>
  <a href="<?= \yii\helpers\Url::to(['category/view', 'alias_cat' => $category['alias']]) ?>">
  <?= $category['name'] ?>
  <?php if ( isset($category['childs']) ): ?>
    
  <?php endif; ?>
  </a>
  <?php if ( isset($category['childs']) ): ?>
    <ul>
      <?= $this->getMenuHtml($category['childs']) ?>
    </ul>
  <?php endif; ?>
</li>