If you are looking to have each Category filter the topics in the topic list, then I suggest using the Discourse Docs plugin and setting that category as your documentation category. This way you can take advantage of the filtering feature that the plugin has. You can see it working on Meta here at /docs
However, if you purely looking to showcase the categories as links to each category, you can try adding the Layouts plugin which is a framework for adding custom layouts widgets on either the left or right sidebars. After adding the plugin you would then install the Category List Widget to showcase the categories.
Alternatively, the Right Sidebar Blocks theme component also looks like a good solution. Though I haven’t tried it yet.