I’m not really sure what your question is.
If you want to create categories, you just go to POSTS => CATEGORIES to create them. Unless you’re creating hundreds or thousands of categories, I don’t get where the efficiency comes into play.
And if you’re referring to how the categories are displayed on your website, WordPress already generates category archive pages. For example, your SCIENCE example will have the archive URL https://www.example.com/category/science/ which will list all posts filed under the SCIENCE category. It will then be up to your theme to provide this “universal menu” listing all your categories, which, again, is a basic feature of EVERY WordPress theme out there.
If I misunderstood your question, please clarify.
I have a Multisite Network.
I would like to provide a Category/One-word descriptor for all sites in the network so that users can filter the SITES by category (not posts).
They’re not actually independent sites – they’re all part of a blogging platform, but the multisite allows me to provide a mini-site to each blogger.
The Universal menu is not standard as it needs to be a Network-wide menu using the SITE categories (If I can ever figure out the best way to do it).
It’s more like creating a Directory of Sites within the network – and providing a menu that goes on them all.