Help: How to display categories as a topic library

Could anyone point me to any plugins to achieve the following –

1) display all the wp core categories in the website as a topic library

2) When one category is clicked, they are able to see a listing of various post types (including custom post types) inside that category – for e.g. posts, books, movies

Here’s an example on what I want to achieve – [https://teamtreehouse.com/library/])

If on the above link one scrolls to the area “Topics”, they can see various topics like A.I. Javascript etc. and then clicking on any of them takes you to a page which lists various types of content within that topic like workshop, practice, course, article etc.

Any plugin to achieve something similar? Should categories be even used to do that? What do you suggest?

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