How can I merge the results of my research ?

I have to suspect you could get something a bit closer to what you’re hoping for with some Autocomplete template customization, but I’m not exactly sure how far that’ll go, given that it’s kind of faceted by default and each section has its own algolia template usage at the same time. Still only one PHP template file that I’ll provide documentation to for customizing.

For a quick overview, you can see the PHP file at https://github.com/WebDevStudios/wp-search-with-algolia/blob/main/templates/autocomplete.php

Customization help can be found at the wiki at https://github.com/WebDevStudios/wp-search-with-algolia/wiki/Customize-Templates