Google has been slowly edging towards it but today the company finally added a Save Tag Group command to the tab right-click menu on Chrome Canary.
The feature needs to be enabled via the Tab Groups Save flag.
It presents the feature is non-functional, but when enabled it will save the tab group to your bookmark bar.
When you switch the toggle off the group will be removed from your bookmark bar.
Tab Groups appear to be under active development at Google and Microsoft at present, so hopefully we will see the feature fully fleshed out in the near future.