CPT using default Categories doesn't display in standard category url

I'm obviously missing something here.

I have applied the standard Post categories to my Story CPT. I can select the custom posts in a Beaver Builder post grid matching the standard category "test". But if I try https://100stories-stage.sitedistrict.com/category/test/ I only see the standard posts with that category not the CPT posts.

1. Is it possible to mix and match post types in an archive loop using a shared standard taxonomy?
2. The actual case here is just trying to retrieve only the CPT "story" since I am not using standard posts at all on this site (other than for testing), using the default categories as in the URL string above: https://100stories-stage.sitedistrict.com/category/test/

If I create a custom taxonomy for the CPT, e.g. "blurp" I can assign both the CPT and standard posts to that category and the results of https://100stories-stage.sitedistrict.com/story-category/blurp/ show both the standard posts and CPT. But I can't do the reverse, using the default taxonomy to display any of the CPT posts.

What am I missing?

Thanks, hope you had a good holiday!