I’m having trouble grasping the use of categories. It seems like I can assign a link only to a single List rather than multiple Categories

The base pillars of SLD are Lists, not individual links. The most common use case scenario of SLD is to create and display multiple Lists of many Links on specific topics. As such, there is no option for a Link (list item) to belong to multiple Lists or Categories. That would make the process of creating Lists slower. For each link you would have to select a List and a Category from drop downs despite the chances of a single List item to belong to multiple Lists are usually not that high. When you have dozens or hundreds of Lists that would become a real issue to create or manage your Lists.

So, if you want a Link to belong to multiple lists or categories, you have to add the the Link as List item for each of the different Lists. Each List can belong to one or more categories. With shortcode, you can output any Category on any page and all Lists that are assigned to that Category will show in that page. The hierarchy is Category->Lists>List Items.