Sideberry extension gives you a lot of what you're looking for. You can have separate tab panels for each container, and a keybinding (ctrl+space by default iirc) that opens a new tab in the current panel and the current container.
Sidebery has been "good enough" for me to transition from Edge back to Firefox, but I wish you could put your Tab Groups into a named folder vs. just having some tabs nested under a "parent tab".
