Hi,
So, the buttons actually work fine. If you click on "yes" or "no" and click on the "next" button, the choice you made is taken into account by HikaShop.
The problem is a display issue. Your template doesn't implement the normal classes of bootstrap like the default template of Joomla 5 does.
I can see on your current website that bootstrap is loaded on your pages but not on your testing environment. I would think this is something changed in your template between both websites.
So I'm not sure what's best to cope with this.
I would first recommend to check what your template provider recommends.