Well, I found where is the problem. The bug comes out of "Enahncements to allow promotions work at variant level" commit ([url=https://github.com/HotcakesCommerce/core/commit/91ef94534e1da0e22f607e934a059f10cda86220#diff-f6cfa8bb4203d547d5000d4578deeb84http://]link here[/url]) about Libraries/Hotcakes.Commerce.Dnn/Web/HotcakesModuleBase.cs file.
At line 211 the previous code on HCC 3.0.1 was
string httpAlias = string.IsNullOrEmpty(PortalSettings.PortalAlias.HTTPAlias) ? PortalSettings.DefaultPortalAlias : PortalSettings.PortalAlias.HTTPAlias;
This pull change adds the culture name to the portal url, I don't know the reason of this change but the problem is that the addition of the culture name parameter on the base url cause the mismatch of the registered routes for APIs calls.
For example the product details view use some javascript function that call the Product/Validate API, but if in the base url is present the culture name it is no more able to find the registered route.
I'm no a programmer and I'm no able to fork and push this on github, but this is the origin of this and [url=https://mmmcommerce.com/Forums/g/posts/t/144/find/unread/HC-3-0-1-upgraded-to-HC-3-1-0]this other[/url] 3.1.0 multilanguage bugs.
For those who need this correction right away, [url=http://95.110.156.198/ForumImages/Hotcakes.Commerce.Dnn.dll]here[/url] you can find the link to the recompiled Hotcakes.Commerce.Dnn.dll waiting for a new official version to be released.