Specifically I'd like to be able to track the number of tabs in a Closed Group via the API. (To avoid having to open the group just to see the number of tabs.)

When the user does “Add tab to group” > Closed group (Firefox; don't know the Chrome equivalent), I'd need to know which group the tab is being added to, or whether it is actually being totally closed instead. (Or the API could expose this info via some other method.)