I wanted to purchase the ATOM RPG: Turdograd and the discount on the site, is not reflected in the cart for purchase.
Wondering if this is just a GOG error or do I have to have ATOM RPG (original) purchased through GOG (and not Steam) in order to reflect this discount.

Nobody answered you. GoG is bad for that and a reason I cannot be bothered posting here as nobody helps much.
Anyway, you’ve probably figured it out by now. You buy from steam you must stay with steam for DLC discounts marked etc.
If you buy here then you must continue to buy for discounts or DLC if it’s so marked.
You can’t split between the two platforms