Hi Dan,
The reason it does not work, is that you are trying it on an archive page. That is not possible, the wordpress core query will always apply on those pages, the plugin cannot change that.
The tutorial you linked is for a custom results page via a products widget, which is placed into a wordpress page – that is different from what you are looking for.
If you want to live filter a products widget, this is the correct tutorial: https://documentation.ajaxsearchpro.com/elementor-integration/elementor-pro-product-widget-live-filter
Basically, the difference is, that you need to place both the search shortcode and the products widget to a single page.