Create tile which lists only Category title and links to Category?

You can create a page for each category, with the name of the category as the name of that page. Then, use the plugin “Page Links To” to “link” each to the category page (usually https://yourdomain.com/maybe-a-directory/category/category-name/).

To target only these pages in the wptiles shortcode, use the attribute id to list the ids of the pages in a comma-separated list.

https://www.ads-software.com/plugins/page-links-to/
https://www.competethemes.com/blog/find-page-id/