custom post types – CPT ui, categories, taxonomies – 2 different archives child of a single page

i’m developing a website for a sports association, that offers courses for basket, volley, calisthenics and ballet (here’s the url: I’m using elementor, cptui and acf.

I am having an hard time figuring out how i can have single pages for the activities (hence a /basket/ page, a /volley/, /ballet/, /calisthenics/) which display some info about the courses, but also have TWO different child archives in them, one for news related to that sport, and one for events related to it.

So what i need to achieve is this (let’s take basket for example):

I’ve tried creating a custom post type for each activity, and then assign to all those custom post types a taxonomy of “type” with “news” and “events” value, but the url is incorrect and the taxonomy is not shown.
Another problem of this solution (somewhat illustrated here: is that the menu item is a “custom link” linked to the post type slug (eg /basket/), to which i’ve assigned elementor builder archive template, and not a “real” page, which imho is not ideal.

I’ve then tried making the static page (/basket/ is now a static page) and create the post type “events” and “news”, but to no avail.

Regardless of what i’ve tried, which may be confusing for the sake of this help request, what would be the best way to proceed? I’ve already asked practically everywhere, but to no avail.
Any consistent help would be greatly appreciated!