You can also display other post types (e.g. WooCommerce products, WordPress posts) with the eCommerce Product Catalog design. To do so, use the post_type attribute with the [show_products] shortcode:
[show_products post_type="product"] – this will display all WooCommerce products (the WooCommerce post type is called product).
[show_products post_type="post"] – this will display your WordPress posts.
The category attribute filters by catalog product categories, so it doesn’t work with other post types.
You can see more show_products shortcode attributes.
How to find out the post type name?
You can find the post type name when you go to the new product/post insert page. As soon as you go to the insert page, check the URL. You will find the post_type parameter there.
To copy products from another plugin into the catalog instead of only displaying them, see Import Products from other content type.