Does “coke” include non-cola flavoured beverages in parts of the US? Here in the UK we tend to call them “fizzy drinks” FWIW.

In the south-eastern US, it's totally normal to order an "orange Coke" (which Coca-Cola either does not make or does not call "Coke" at a minimum).

I can kind of see how that came about—my kids would assume that any soda I drank was a diet coke and would refer to orange soda as orange diet coke.

In the American South, you're likely to hear "coke" regardless of whether it's actually Coke, or even cola-flavored. It's "pop" up north, and "soda" in the northeast and southwest (plus a couple of pockets near Milwaukee and St. Louis, which would otherwise be "pop" territory - fascinating stuff).

Whenever I would visit family in Louisiana, it was pretty common to go to restaurants, and even at places that exclusively served Pepsi products, asking "what kind of Coke do you want?"

Yep. Coke is every carbonated sugar drink. You have to get all the way to la croix for it to stop being a coke. South-Eastern USA aka "The American South"

Here's some interesting regional US dialect maps:

https://www.rd.com/list/regional-sayings-phrases-words/