Is it possible not to display some accounts in Cozy Banks (such as an account with a power of attorney)?

This is indeed possible, by using the groups. The app Cozy Banks allow you to put accounts in groups, and to display only some of these.

To create groups, go in the settings menu on the left side of the website, and you will be able to create groups in the third tab.

Then, click on the little arrow next to 'all the accounts' ('tous les comptes' here) to select which groups you want to display.