custom taxonomy count always zero

I regiested post_type and taxonomy using below code :

        public function cptui_register_my_cpts_site()
        {
            /**
             * Post Type: 网站优化信息.
             */
            $labels = [
                "name" => __("网站优化信息", 'joa'),
                "add_new" => __("新增网站优化信息", 'joa'),
                "singular_name" => __("网站优化信息", 'joa'),
                "add_new_item" => __("新增网站信息", 'joa'),
                "edit_item" => __("编辑网站信息", 'joa'),
                "new_item" => __("新增网站信息", 'joa'),
                "view_item" => __("查看网站信息", 'joa'),
                "view_items" => __("查看网站信息", 'joa'),
            ];

            $args = [
                "label" => __("网站优化信息", 'joa'),
                "labels" => $labels,
                "description" => "",
                "public" => false,
                "publicly_queryable" => false,
                "show_ui" => true,
                "show_in_rest" => false,
                "rest_base" => "",
                "rest_controller_class" => "WP_REST_Posts_Controller",
                "has_archive" => false,
                "show_in_menu" => true,
                "show_in_nav_menus" => true,
                "delete_with_user" => false,
                "exclude_from_search" => true,
                'capabilities' => $this->capabilities,
                "capability_type" => "post",
                "map_meta_cap" => true,
                "hierarchical" => false,
                "rewrite" => ["slug" => "site", "with_front" => false],
                "query_var" => true,
                "menu_icon" => "dashicons-admin-site",
                "supports" => ["title"],
                "show_in_graphql" => false,
            ];

            register_post_type("site", $args);
        }

        public function cptui_register_my_taxes_in_charge()
        {
            /**
             * Taxonomy: 关键词.
             */
            $labels = [
                "name" => __("负责人", 'joa'),
                "add_new" => __("新增责任人", 'joa'),
                "singular_name" => __("负责人", 'joa'),
                "add_new_item" => __("新增负责人", 'joa'),
                "edit_item" => __("编辑负责人", 'joa'),
                "new_item" => __("新增负责人", 'joa'),
                "view_item" => __("查看负责人", 'joa'),
                "view_items" => __("查看负责人", 'joa'),
            ];

            $args = array(
                "label" => __('负责人', 'joa'),
                "labels" => $labels,
                "public" => false,
                "hierarchical" => true,
                "show_ui" => true,
                "show_in_menu" => true,
                "show_in_nav_menus" => true,
                "query_var" => true,
                // "rewrite" => array('slug' => 'in_charge', 'with_front' => false,),
                "show_admin_column" => true,
                "show_in_rest" => false,
                "rest_base" => "",
                "show_in_quick_edit" => true,
            );
            register_taxonomy("in_charge", ['post','site'], $args);////////////////
        }

register_taxonomy(“in_charge”, [‘post’,’site’], $args);

if i use register_taxonomy only in site object type , the in_charge taxonomy count value not increace , always is zero.

if i add post , the count value will auto updated .

Is this is a bug here ？