Maybe in the future "Open tab" sync will be enhanced with tab group information, but I suspect that might be quite a ways down the road. Mozilla has a product suggestion site at https://connect.mozilla.org/ where you could vote for this idea or, if no one has posted it yet, create a new idea submission (at https://connect.mozilla.org/t5/ideas/idb-p/ideas). For now... extensions can read tab group information, so someone might create an exporter for grouped tab information. For example, this might create a "bookmarks.html" style file you could open in a tab (to manually open links as needed), or a compact data file that you could exchange between different installations to auto-load the tabs. Those aren't as convenient has having that direct access through Sync but could be useful as an interim measure. Do you have any thoughts about the design of such a tool? ''Extensions also can share data via sync, but only a modest number of characters is allowed, so there would be a limit on the number of URLs that could be shared this way.'' (https://developer.mozilla.org/docs/Mozilla/Add-ons/WebExtensions/API/storage/sync)

There is in fact an idea on mozilla connect that could use all the votes it can get so we might see this feature sooner rather than later :P https://connect.mozilla.org/t5/ideas/synced-work-spaces-or-synced-tab-groups/idi-p/22999