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 present it is unclear exactly what the feature does, but it may be that it ensures that a tab group is preserved between browser sessions.
This is of course already the case if you set Chrome to “continue where you left off” in Chrome Settings.
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.