Satoshi Nakamoto invented Bitcoin in order to avoid any need for trusted third parties.
Cryptocurrency exchanges like Coinbase or Binance are examples of trusted third parties.
From the above, I would not expect trusted third parties to be especially facilitated by the Bitcoin network protocol initially created by Nakamoto, nor especially facilitated by what many regard as the reference implementation of a Bitcoin node (Bitcoin-core) which was originally developed by Nakamoto.
I would expect commercial businesses, such as those two, to have employed software developers to create proprietary closed-source software that suits their business objectives. They might, or might not, have used elements taken from open-source Bitcoin projects - where they can do so without violating the licence terms.
Commercial business tend to keep confidential the details of their internal systems. Especially those which relate to control of money. It should not be a surprise if they do not reveal exactly how they create, for their customers, the things they call "wallets".
Some of these businesses may have their own APIs that can be used by resellers of their proprietary services, or by others. I would expect that users of these APIs would have to seek documentation and support from the businesses concerned.