Do they sync?
If your use case is not covered, you surely can write a WebExtension to provide the functionality. Containers as well as sync are exposed in the API.
Container settings (names, colors, icons, assignments) should be synced (if not, please file a bug). Open tabs will be synced, not sure how they will open on another machine (considering URL-to-Container assignments should be synced, they should open in the respective containers – maybe there's a possible improvement here).
I expect the different Cookie stores to be synced as well, if not, that's a bug.
Also, changing a container's color does not change the color shown on existing tabs.