I enjoy containers a lot and want to add a piece of idea to the project.
Regarding the privacy protection provided by containers, it would be interesting to save history or cookies in one container and not in another. For instance, I might want cookies to survive in my Finance container, so I don't need to click the cookie banner each time I go on my bank's website, but not wish to be tracked in my Shopping container since I hate personalized ads. The same goes for search, history, download...
In any case, nice job.
PS: of course, another related issue would be to be able to clear history, cookies, etc. by hand for a given container, or even use the "Forget" option for a given container.