You're not missing anything - and good question, now I know that the wording might be triping people up. This add-on organizes the tabs you currently have open (auto-merging duplicate groups, grouping by site, etc.). It doesn't store closed groups itself.

Saving a group to reopen later is actually built into Firefox now (141+): instead of just closing the tabs, right-click the group and choose "Save and close group." It then lives under the "List all tabs" button and clicking it the a closed group from in there brings the whole group back. Just closing the tabs won't keep the group; only that "Save and close" option does.

Hope that clears it up and thanks for trying the extension!