“add to cart” links css class “ajax_add_to_cart” doesn’t show in woocommerce in widget sidebar

At last i solved it myself. Hope someone will get benefit form this answer. I merge $default variables all array (quantity, class, attributes) directly into link. I changed whole block of if ( $product ) {}.

if ( $product ) {
    $output .= sprintf( '<a href="%s" data-quantity="1" class="%s" %s>%s</a>',
    esc_url( $product->add_to_cart_url() ),
    esc_attr(
        implode(
            ' ',
            array_filter(
                array(
                    'button', 'product_type_' . $product->get_type(),
                    $product->is_purchasable() && $product->is_in_stock() ? 'add_to_cart_button' : '',
                    $product->supports( 'ajax_add_to_cart' ) ? 'ajax_add_to_cart' : '',
                )
            )
        )
    ),
    wc_implode_html_attributes(
        array(
            'data-product_id'  => $product->get_id(),
            'data-product_sku' => $product->get_sku(),
            'aria-label'       => $product->add_to_cart_description(),
            'rel'              => 'nofollow',
        )
    ),
    esc_html( $product->add_to_cart_text() )
    );
}