Woocommerce – Products belonging to multiple categories and hiearchy

Hi, i’m developing an e-commerce for a record shop with WP, elementor and woocommerce.
I need to set up many products which belong to different genres (almost always more than one, being it focused on electronic music).

I’ve tried creating product categories, like this

– Techno
– –Dub Techno
– –Deep Techno
– –Acid Techno
– House
– –Deep House
– –Tech House
– Downtempo

The issue with that is that when a product has like 3 categories, the breadcrumb mess up.
Also, it shows the categories on the products in the archive page, which i’d rather not, since it doesn’t show them all.

There are many vinyls that belong to eg. Deep House (which is a subgenre), hence to House as well (as it’s the parent), and Downtempo (another 1st level genre).
This really seems to mess up things!

I’ve then tried adding a custon taxonomy just for genres, but that’s just the same as categories ofc.

I’ve also tried to avoid using categories and using an ACF field instead, but the problem with this logic is that i don’t know how i could handle the child elements of the menu then.
The menu will be like this:

Catalog

– House
– Techno
– Breakbeat

and so on, so just the first level of nestling.

How can i achieve that? Is there a way to make specific tags *childs* of a specific category? I’m really lost.

The shop page and subcategories (the genres) will need to have a filter that has 2 parameters:
1: genre
2: style (if present, some genres won’t have substyles)`

The page I need help with: [log in to see the link]