Hello,
Sorry to hear about the inconvenience.
Actually, after you mentioned the concern we confirmed it from the Test Site. There we enabled the updated option of Product Variations as Single Products, then checked back the Shop page, and there the Compare and Wishlist Icons were showing on those individual Variant Products too. Here is the Shop Page URL from our Test Site, you can see for yourself too: https://blackpearlspro.com/woodmart_support/shop/
Here a Product named “Eames plastic side chair” is showing as Individual Variants and you can see the Wishlist and Compare icons are showing and working perfectly fine.
So, there might be some third-party Plugin conflict on your Site. So, can you please once try deactivating all the third-party Plugins on your Site? If the issue gets resolved, then reactivate them one by one to see which Plugin is causing the issue.
Best Regards.