I understand that confidential transactions hide the amounts sent and received. But what does the new taproot privacy technology hide for bitcoin?
Taproot replaces having the script (say, for a smartcontract) written in the tx itself. It uses the MAST scheme to make it so that the redeem script only needs to validate whatever is in the MAST structure, not have the whole contract code, evaluate it and release the coins. (I'm not sure if I'm technically accurate here, I'm not a developer)
It enhances privacy because every tx (be it a smartcontract or not) will look the same. So the privacy benefit is that no one can see that a given tx you sent is actually part of a multi-sig contract, for example. See more here
Taproot allows inputs to hide the fact that there is a script specifying a contract. If sufficient parties involved in that contract agree and cooperatively spend the Bitcoin, that input looks just like any other input, including ones that do not have contracts and have only one person.
This helps privacy as the conditions of a contract are hidden. This also makes such transactions smaller which will save on fees.