How safe is my ETH when staking in a pool?

I'm trying to get a basic understanding of how pool staking works, as I want to get a clear picture of any risks.

How accurate is this:

When anyone delegates ETH to any staking pool, is all of this ETH sent to the same smart contract address? Are the delegators given a token e.g. ETH_staked_token to represent their share of the ETH stored in the smart contract? They would then use this ETH_staked_token when they want to take their ETH out of the smart contract?

The pool/node operators have no "physical" access to the delegators ETH? The ETH is just assigned to them, without giving them direct access?

What are the risks for delegators? Ethereum staking smart contract hack for example? Presumably this is the only risk, assuming the ETH_staked_token is a thing and it's stored safely e.g. on a ledger device.