Additional context from meeting with @JWheeler-WMF

• if the categeries are consistent, the team can think of suggesting templates based on categories
• are there any specific kind of templates more used by newcomers vs. experienced users.
• templates present on most wikis and transclusion count by wiki (for example, cite web is on 287 language wikis; Wikidata items can be used)
  • helps to identify the most commonly used templates across wiki

Yes, it is a feature we're actively designing and plan to start eng work in july.

Hi @mpopov . Is there a way for me to DIY an answer to this question?

How varied are template categories across wikis (ie, does EN-Wiki have 20 categories, whereas de-Wiki have 42?)

Kind of? Categories are…a giant unstructured, manually-maintained mess and inconsistent across languages. (In general, not just specific to templates.) Categories can also have layers upon layers of sub-categories nested within each other, and there's not an easy way to get them all.

Consider https://en.wikipedia.org/wiki/Category:Wikipedia_template_categories which is supposed to be "a category that contains all categories of templates, listed alphabetically" – it is linked to 58 languages and German isn't one of them. There may be a category like it, but not linked.
33,040 total on enwiki, 2,987 total on ptwiki

Then there's https://en.wikipedia.org/wiki/Category:Wikipedia_templates which "groups templates according to use, type, etc." and that's linked to 244 languages, one of which IS German https://de.wikipedia.org/wiki/Kategorie:Vorlage:
You can expand each sub-category and see how many sub-categories there are and how many templates (pages) there are in each sub-category.

A DIY approach would be to explore these pages across languages, ideally with someone who reads those languages.

Unfortunately there's no ready-to-use self-service dataset for totally valid questions about the content on Wikimedia projects. Even querying would be difficult because category names & IDs are inconsistent across languages. That second "Category:Wikipedia_templates" example if you had a query that retrieved all the sub-categories (assuming you didn't want to also get sub-categories of each sub-categories, etc.), you'd still need to know the name or ID associated with that "parent" category for each language you're interested in.

Thanks @mpopov I think this answer sufficiently answers our question. Please correct me if my assumptions are wrong:

Given the extremely high variance in category usage across wikis (33,040 on enwiki, 2,987 on ptwiki, and a whole list of subcategories and even category structures across wikis, we cannot build a scalable solution by category or subcategory. While we could build a model that's useful for a single wiki, we would not be able to scale this to many.