When we send it to Incognito or Shield it, where is the Monero or Eth we sent actually stored? Is any in Cold storage vs hot?
For ETH/ERC-20 its stored within a bond smart contract. For XMR, BTC, BNB, etc. it is currently stored in a hot wallet, sends and receives constantly.
Here are some details about ongoing work towards a trustless bridge for currencies without smart contacts: Incognito's trustless bridge V3 with Ethereum bond contract
Hope that helped.