Nightly has this built in actually, though the icon looks a little different. Enable it in about:preferences#general in the Tabs section. The icon looks like a file cabinet.
The built-in functionality doesn’t have nice things like “always open this site in such-and-such a container”.
Indeed: that’s how I use it. (I use this to keep work and personal stuff separate because of a couple of services that don’t support multiple simultaneous logins.)