How to insert variable product with PHP?

When I try to use WC_Product_Variable() the variations are created but somehow not properly synced / assigned. Deleting and creating the variations from /wp-admin/ works but how can I properly add variations to a product with PHP code?

I currently have this:

public static function create_wc_variable_product($products_to_import, $common_items, $variant_name)
    {
        $unique_short_descs = array_unique(array_column($products_to_import, 'short_desc'));

        $product = new WC_Product_Variable();
        $product->set_name($variant_name);
        $product->set_status('publish');
        $product->set_description('Variable Product Description');
        $product->set_short_description('Short Description');

        $attribute = new WC_Product_Attribute();
        $attribute->set_id(0);
        $attribute->set_name('Variation');
        $attribute->set_options($unique_short_descs);
        $attribute->set_position(0);
        $attribute->set_visible(true);
        $attribute->set_variation(true);

        $product->set_attributes([$attribute]);
        $product->set_variation_attributes([$attribute]);
        $product->save();
        $product_id = $product->get_id();

        foreach ($products_to_import as $product_data) {
            $variation = new WC_Product_Variation();
            $variation->set_parent_id($product_id);
            $variation->set_attributes(['Variation' => $product_data['short_desc']]);
            $variation->set_status('publish');
            $variation->set_regular_price(isset($product_data['list_price']) ? $product_data['list_price'] : 0);
            $variation->set_sku(isset($product_data['article_nr']) ? $product_data['article_nr'] : null);
            $variation->save();

            update_post_meta($variation->get_id(), 'hwp_var_gtin', isset($product_data['technical_details']['GTIN']) ? $product_data['technical_details']['GTIN'] : '');
        }
    }