Thank you - this was a great tip.
In case it helps anyone… I also found you can get ONLY the first child Categories by putting {echo:get_queried_object_id}
In both PARENT and CHILD OF - in the query.
In a category archive, this returns just same-level categories, enabling you to ‘walk down’ the category tree and show ‘next branches’ to go down - with a single template.
e.g.
Cat_Main
SubCat 1 - Subcat a, subcat b, subcat c
SubCat 2 - Subcat X, subcat Y (subSub Y2, Y3, Y4), Subcat Z (subsub Za, Zb, Zc)
On Cat_main page you see SubCat 1 and SUbCat 2
On SubCat 2 page you see X,Y,Z
On subcat Y page you see Y2,Y3,Y4