The use of localStorage by the client-storage flows should be tested using a browser. The idea is to add a Controller to the IdP which wraps access to a StorageService for use by the integration/Selenium tests. The client-storage tests will read/write to the StorageService using the Controller, then run the client-storage flows, and then check cookies or localStorage TBD.
A certain amount of gymnastics with Maven, the testbed, the integration tests, and idp-conf appears to be necessary to get this all working. There probably is a better way to do it.