Thanks for the proper details.
1. You had grouping turned on, which resulted in trimming the categories from the results – since it's not possible to group the category term to a category (because it's the category itself).
2. The plugin cannot override the layout of the default search results of the theme, it's unfortunately not possible in wordpress. It can only override the result items – so you get the same results as in the ajax search process. (except for terms and categories, those can't be displayed on the wordpress search page)Best,
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