The most common Shopify theme bug after an app is uninstalled. Shopify removes the app, but the code it pasted into your theme stays behind. That leftover breaks the product page's script, so picking a size and pressing Add to cart silently fails. Switch between the broken store and the fixed one and try it.
Liquid error ... Could not find asset snippets/reviews-widget.liquid, and the console shows Uncaught ReferenceError: ReviewsWidget is not defined in the product script. A search of the theme code finds the leftover {% render 'reviews-widget' %} tag and the app's script include.sections/main-product.liquid and layout/theme.liquid; the variant script now runs, so the size picked is the size added.