I find POP->DAD a little odd, because I've never (as an American) heard anyone say 'pop' referring to their father. 'pops'? yes. Now, POP->SODA, would not surprise me in the least.
“Pop” gets used in the UK sometimes but I’ve only heard it in northern England. Never heard Soda anywhere in the UK though, apart from the specific case of cream soda.
In Aus I use Pop to refer to my Grandad who was british. I do think it was to help with confusion with which grandparent I was referring too, was it my dads dad or my mums dad
It's an older generation thing. See Pop Tate in Archie comics [1], for example; the soda fountain guy. Guessing it's probably derived from Papa, like Pa, Paw (hillbillies), etc.