The caffeine is coke is synthetic. Using synthetic caffeine is cheaper than extracting it from coffee.

To the best of my knowledge, the only place where they still use caffeine from coffee is Japan.

Ah, didn't realize this. I used to work at a coffee roaster and at the time was told the caffeine removed from decaf beans via the swiss water method was then sold to soda companies.

Caffeine is cheaply synthesized, and that’s almost certainly what soda manufacturers use in their products.