If there are many Category items when you select the taxonomy in the Builder, you can deactivate all plugins except Meta Box, MB AIO, and WooCommerce. Then select the second Category item, it is the Product category, the first is the Post category. Let's take a look at my screen record https://www.loom.com/share/4d72113b73ad47488af87c2619338d10.
If you select to show the field for taxonomy, it will show the field in all terms settings include the child term (child category).
Regarding the field still shows for the taxonomy when you select another type like Posts, could you please take some screenshots of this problem? I've tested on my site but do not see the problem like that.
The Custom Fields display on the category (taxonomy) admin but not the product admin. Shouldn't they appear there as well? What I am looking to accomplish is to hide all custom fields in Taxonomies and then have the custom fields appear on select subcategories (terms) that relate to the products within that subcategory. Then filter them accordingly via FacetWP.
Categories (taxonomy - all products appear)
- Toys (taxonomy - all products appear that are under this term)
-- Action Figures (term - all products appear that are under this term)
--- Darth Vader (product)