There are two different apps - Coinbase (exchange) and Coinbase Wallet. The last one is Coinbase Wallet is a non-custodial product. So it doesn't keep any users data.
Yeah I found it.
The privacy policy seems to indicate that they are able and will store certain personal identifiable information. While they *probably* won't have access to your private keys, you cannot assume that they are not actively tracking their users as well. Their privacy policy allows them to collect certain information and also share them to law enforcement if necessary.