2 videos to demonstrate the problem. In both cases, the caching plugin is enabled (tried different ones, the problem remains when the Woodmart theme is activated).
1) Video #1. Installed the default “Storefront” theme. As you can see, counters work fine in both places: a) class=”count”; b) class=”product-quantity”.
2) Video #2. Activated the Woodmart-6.2.4 theme (not a child theme): a) class=”wd-cart-number” – the product counter with a class from the Woodmart theme does not work correctly, i.e. every time you reload it shows the same value that was cached the first time; b) class=”product-quantity” – works correctly, I believe, via WooCommerce script “plugins/woocommerce/assets/js/frontend/cart-fragments.min.js”.