Just using the standard category output, with appropriate styles added, would solve (or make easier to solve) several bugs, including T181344, T175713, and possibly T186089 & T175716.
- Adding appropriate styles and adjusting the output slightly can make it display as a column in the sidebar, but this can be overwhelming if there are many categories on a page.
- The alternative would be to show the regular output at the bottom of the page, but consideration needs to be given as to whether this would be in addition to or instead of the sidebar (see also discussion in T160645)