How do I build a query that counts pages by category or subcategory?

1. Make sure semantics is enabled for category pages,
2. define Template:Count pages in category as {{#ask: [[Category:{{{1}}}]] | format = count}},
3. insert query {{#ask: [[:Category:+]] [[Category:Parent category]] | link = none | format = template | template = Count pages in category}} into your page,
4. submit and wait forever until the page is parsed.

Alexander Mashin^talk