I've created a quick and dirty FF extension that will essentially do the above. I use ManicTime + Multi-Account Containers + Simple Tab Groups -- and that's been pretty good to keep a sprawling bunch of tabs in check, and has worked fairly well with ManicTime to autotag. However, I was really wanting to be able to autotag based on the current tab's container rather than just the group I was currently in.

For instance: have one tab group that represents an MSP I contract to with multiple tabs for their different clients open in that group in their own sub-client containers. I wanted to autotag based on the sub-client (container), not the client (tab group) and this extension allows for this.

Its in the process of getting published to the FF extension market. If you're interested, I'd love a little beta-testing. Its free, and will always be free.