Questions about two very similar cookie recipes

I want to replicate the Levain Bakery cookies, and I've found two recipes, which are pretty much the same, except for this: Recipe #1 -1tsp of cornstarch -1tsp of baking soda https://kirbiecravings.com/levain-bakery-chocolate-chip-cookies/

Recipe #2 -1tsp of baking soda, -1tsp of baking powder. https://www.delscookingtwist.com/2018/05/22/levain-bakery-chocolate-chip-cookies/

The thing with recipe #2 is that it asks for homemade cake flour, which is 1 cup (120g) of all-purpose flour. Remove 2 tablespoons of the flour, and add 2 tablespoons of cornstarch to the flour. Sift the flour and cornstarch mixture over a medium sized bowl 3 or 4 times

So, assuming store-bought cake flour has cornstarch in it as well, is it really necessary to add more of it, like Recipe #1 calls for?  Why would you use baking powder instead of more cornstarch in Recipe #2? Also, recipe #1 calls for more regular flour.

I really want to make this recipe, but I need to figure this out first. Besides this, the recipes are basically the same. Thank you for your help :)

bon appetit