By default, these types of pages are not supported by Elementor. These pages are “auto-generated” by WordPress and don’t have “the_content” filter that offers the posibility of editing them with Elementor.
The current workarounds are:
Elementor PRO has a powerful feature called Theme Builder which is able to override these types of pages entirely and maintain their query vars, to be compatible with other plugins and tools. More at https://elementor.com/blog/introducing-theme-builder/ .
Usually categories/archives contain a grid. It’s the most important part of the page. As a companion, you can use a Page Cover ( more here https://support.reytheme.com/kb/how-to-create-page-covers/ ) and offer the page a custom layout
By enabling Products as editable post types in Elementor settings eg: https://d.pr/i/FNHa2X , you will be able to insert Elementor elements into the product page’s description block eg: https://d.pr/i/WgueEA .
Rey has a pretty cool feature that allows inserting generic global sections into product pages after the product summary. They can be added via Customizer > WooCommerce > Product page – Content eg: https://d.pr/i/CFu5FZ .
They can also be overridden in the product’s individual settings eg: https://d.pr/i/KmJPo7 .