@BtaWlf‘s solution does not work for me. I am on 133.0.3 (64-bit) (stable), the "browser.tabs.groups.enabled" is properly enabled but no "add tab to new group"option.
I do not know if there are some requests and the developers are looking here for ideas and suggestions, but I would love if it will be possible to pause and release resourses from the groups that are innactive.