Hi,
Since you configured a post code and a zone in your tax rule, the tax rate will only apply once you're logged in and you're on the checkout and enter your billing address with the zone and post code that you entered in the tax rule.
Your screenshots are from the products listing and the product page. But it's normal that they don't show the price with tax as you probably didn't yet log on your website or your user account maybe doesn't have any address or the address doesn't have the same post code/zone.
So in short, if you want to have the prices with tax on your products listings/product pages, you don't want to set a post code in the tax rule and either you don't want to set a zone, or you want to select that same zone as the "main tax zone" setting of the HikaShop configuration.