What kind of privacy does Taproot give bitcoin? I understand that confidential transactions hide the amounts sent and received. But what does the new taproot privacy technology hide for bitcoin?
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.