[[Module:compound/templates]]: derivsee

That's what the class= argument does.

Does the class argument apply to just the category name line, or to the whole thing?

I don't know. But it's what is used to apply the sc= parameter of the template currently.

I looked into it and the class "CategoryTreeLabelCategory" is used for the category link, while "CategoryTreeLabelPage" is used for the entry links. So these are the ones we want to target. I'm not a CSS expert, but hopefully someone can figure out how to override "CategoryTreeLabelCategory" to inherit the "Latn" class.