How exactly are public/private keys stored?
No they are not stored, the child keys are calculated from the master when needed as they are deterministic, not random. 

Here are some references:    

https://www.oreilly.com/library/view/mastering-bitcoin/9781491902639/ch04.html#_deterministic_seeded_wallets

https://learnmeabitcoin.com/guide/hd-wallets