Custom query multiple sources different badges

[fivehorizons79]

Dear all,
I'm working with E.Pro and Events Manager.
I'm using the posts widget in order to show the list of news (posts) and events (events coming from EM plugin) together in the same page sorted by post date thanks to the following custom query:

add_action( 'elementor_pro/posts/query/eventi_HP', function ($query){
    $query->set('post_type', [ 'post', 'event' ]);
    $query->set('orderby', array('post_date'=>'DESC'));
    }
    );

I like very much the badge option but I can choose only between "Post categories" and "Events categories" and obviously appears only the selected one.
I would really appreciate to have "post category" badge on the posts and "Events category" on events posts.

I suppose to have to force the taxonomy into the loop but honestly I'm not so good in coding.

Any kind of help will be really appreciated.

Ciao
Alberto