Not sure if you are already aware of it, but just throwing it out there as it’s not very obvious.
Depending on the theme you are using, sometimes the variables in your product-card.liquid file may refer to the product in a different way than “product”. So check for that specifically. I have seen different variations, in the two themes I’m using for my stores, it’s “product_card_product” and “prod”. So in my case, it would say {% if product_card_product.tags contains ‘Multibuy’ %}
