How can I achieve this:
When DirectoryOpus closes (when Windows is shut down), DirectoryOpus automatically saves the actual Lister folder-tab configuaration (i.e. all opened folder tabs) to a preconfigured folder-tab-group (e.g. LastFolderTabs), so when I continue my work the next day I could optionally load the LastFolderTabs group to have the same folder-tabs available as the day before. Of course I could do this manually, but an automation would be more comfortable.
Maybe not in the exact way you're expressing it (i.e. auto-saved "Folder Tab Groups") but Opus has several categorizations of saving and loading lister configurations. The one most relevant to what you're looking for is probably the 'Layout' system.
There is the sometimes misunderstood 'Default' Lister layout... which while you 'can' configure to load up when using either of the double-click methods mentioned above... is always what gets loaded when you launch a lister using the Opus desktop or Quicklaunch shortcuts. To get the effect you're looking for, you can select the Update Default Lister automatically when closing a Lister options on the Preferences->Listers->Options page.
What you would then do after closing your 'last' lister of the day... positioned and setup the way you'd like to return to it then next day, is launch that next days lister using one of the shortcuts...
The kicker is, if you're working throughout the day, then close your lister in the state you'd want it saved in for tomorrow (or just 'later')... but then open another 'regularly' configured custom lister layout... when you close THAT lister it becoimes the 'new' default.
Now beyond that, if you're like me and 'generally' have a particular set of starting folders that you'd usually like to see displayed when you open listers throughout the day, I'd suggest that you setup a lister in the way that you would like, and then save that as a custom layout using the Settings->Lister Layouts->Save This Lister... menu option. You can then configure the double-click on desktop (my fave) and double-click on tray icon methods to load that saved layout...
Nudel would have explained this in a fifth as many words... but yet I'm not done 
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You could also go the 'other' way and create a specific saved layout, along with a button that you could manually press to update that lister with the current state... a button command like Prefs LAYOUTSAVE=single LAYOUTNAME=Recall would do the trick... of course going this way you're just 'trading' the possibility of forgetting to click the button for the possibility of opening another 'regular' lister AFTER having closed your lister in the state you wanted the default layout mentioned above.
Then again, you could use BOTH methods to have each act as a safety catch for each other... see what you think.