I don't use containers myself, but I have a thought. I suspect the information about containers to use for certain URLs is stored in the Multi-Account Containers extension data instead of in the database where the bookmarks are stored. So if that is true, we probably need the extension to generate the customized bookmark list -- from its own toolbar button or custom sidebar -- because extensions can't modify the built-in menus. But maybe there is a deeper level of integration I'm not aware of.