I am not really sure Patroni has anything to do with the persistence of data. It just uses etcd, zookeper or consul to elect a master in case of a failover and uses their key value store to save the information about the current master. Its upto you whether you keep your database on a container or not. And how the data is managed by the container.
This talk by Josh Berkus explains how Patroni works pretty well.
https://www.youtube.com/watch?v=OH9WSEiMsAw