Results page template of Search API module
Search API filters and results are displayed using views - so you need to override the views template.

So if you create a view page for your search called "Search API" (search_api) - and the machine name of that view is page - then you can add the following file to your theme:

my_theme/templates/views-view--search-api--page.html.twig


You probably want to start by copying in the contents of core/modules/views/templates/views-view.html.twig into the above template file and start tweaking it from there.



For help creating the actual view you may find these links helpful:


https://www.drupal.org/docs/8/modules/search-api/getting-started/search-forms-and-results-pages/searching-with-views-0
https://sweethoneycode.com/custom-search-with-search-api-and-views-drupal-8/