Haha. Can confirm. I am from Arkansas, and before they passed on, my grandparents usually kept a variety of soda in the house for us grandkids (they never drank it, they of course loved their coffee).
it didn't matter what kind of soda was actually in the fridge, every soda was a coke. my grandma would grab a dr. pepper or a pepsi and say "ya'll want a coke?"
Businesses often use “soft drink” regardless of region but people rarely say that (but it’s not that weird if they do)