Hello,
I have checked your site and noticed that the product categories are currently hidden globally from the Theme settings, which is why they are not appearing on the shop page as well.
To properly target only the Products (Grid or Carousel) widget, we first need the global setting to be enabled so we can isolate the widget-specific styling.
Please, enable product categories globally again from Theme Settings > Product archive > Products loop > Show product category
After that, I can check the carousel widget specifically and provide you with the exact CSS solution to hide categories only there without affecting the shop/grid pages.
Alternatively, if you prefer, you can share WP login details and I will inspect it directly and give you a solution.
Best Regards