Well,

“Repair Categories” was the answer.

I was afraid of using it because everything else was just working fine.
And the wp_options record for wppizza seemed to be ok (the category_sort part at least)

I don’t really know how I “broke” them.
We erased the default categories and created new ones (me, as an administrator, and another user, with Editor role)

Anyway, i’ll keep an eye on this.
Many thanks for your support 🙂