Hi,
There is no easy way. It requires customizing the Joomla results pages. The thing is that the search results and tag results can display things other than products. It can be Joomla articles, or other Joomla extensions content.
So Joomla just display the basic information (name and description basically). Having it display an add to cart button would be difficult since it only applies to the results that are HikaShop products and Joomla doesn't have a mechanism to request how to display each search result based on its type.
However, here is an alternative:
Instead of using Joomla search/tag system, you can use HikaShop filter system:
www.hikashop.com/support/documentation/1...-filter-listing.html
You can for example create a text filter on the product name and product description (and other columns if necessary) in order to search on the products data similarly to what the search system of Joomla would do.
However, the results will be displayed as a HikaShop products listing and thus you'll have the same display options as the normal listings of HikaShop and so you get can the exact same look.
And instead of tags, you could create a custom product field of the type "multiple dropdown" to be able to select tags in that custom field, and then create a filter on that custom field to get a similar thing as the tag page.