Containers isolate more than just cookies, they isolate all local storage. So each container acts like 3rd-party cookies are enabled, they get saved, everything

Containers isolate more than just cookies, they isolate all local storage. So each container acts like 3rd-party cookies are enabled, they get saved, everything works even when silly website authors use 3rd-party services for authenticaton, etc. But it's all isolated, so the sites in one container don't see any of the storage in another.