Make archive page show up in search results?

The issue is that an archive isn’t a post, it’s not something that can be shown in the loop. On your search results page, you’ll have to add some code to search categories for a similar name. You can accomplish this with the generic get_terms. Pass the searched term as the name__like argument (or maybe description__like if you want to store more store-specific stuff that could show in a search). get_query_var( 's' ) will give you the search term to pass.