I installed the Monterey Public Beta today and the tab groups are working for me in that environment, but still not in Big Sur.

What I find interesting about this is that I have 2 MBPs (2016 and 2020 both Intel) and the 2020 is working as expected but the 2016 is not. I don't know what that means in the big picture, but it is not widespread on all Intel Macs. Good stuff...