Hi,
I indeed did my tests on the listing page since that was the link you provided and where you had the issue.
And on the listing page, the cart module does display fine in the bottom position and doesn't display in the slider of the template. So it doesn't indicate a problem with the template.
And regarding the product page link you gave, it doesn't even display the product page content itself. That's not normal. The default templates of Joomla are not supposed to not display the content of the product page. So something is messing up the default templates too on the product page which would explain why the cart module does display there. Hard to say what is the source of the issue, but what's stranger is that the product page content does display for your template and not the default ones so it's not like HikaShop is not sending the content of the product page to the template... I don't knwo what you did but a normal Joomla website isn't supposed to do that. It might be linked to system plugins interfering with the display. You could try disabling them one by one.
But that's not linked to the cart module not displaying on the left slider once you had a product in the cart on your listing page.
That's clearly independent from HikaShop.