I often just save the whole window and imeddeately restore it again in such cases.

Yes, this functionality is planned, and i hope very soon.

Meantime i can only suggest disabling the "Continue where i left off" option in the Chrome settings

Do you have "Continue where i left off" option enabled in the Chrome settings?
If yes then it's chrome reopen all your tabs that were open on last closed normal window every time you create any new window after a period with no normal windows was opened (Tabs Outliner window is not "normal" and if only it's present Chrome think that actually it's an end of the previous session ).

This is known problem without any simple solution... though i plan of course to deal somehow with this situation soon. Yet not very sure how, as it's the Chrome who reopen the additional tabs

Also, you can go directly to native Chrome context menu (with Save as.. item and so on) by right-click with Cntrl pressed (as this is mentioned in a context menu by the way).

But.

I am really recommended to try set up a Google account for Chrome sign in, for example using not your main email, but some other, specifically for that purpose. You then can disable all synchronization features when you SignIn to chrome, using this email, so no your bookmarks or passwords will ever be transferred to Google servers (they anyway transferred in an encrypted form, and cannot be accessed by Google if you configured so, but, just in case you are not comfortable with this idea you can just disable all types of synchronizations altogether)

So, this way you will be able as support the development by buying a paid mode key, or, if you decide not to do so, anyway, the Backup tab in Options have more handy and more robust way to export and import data using text files (and this export everything, including content of collapsed nodes, wich is not exported by Ctrl-S export), and it's work in free mode, manual backup to Google Drive account also works and is possible only if Chrome is signed in, as it depends on its autorization infrastructure for this.

Best Regards
Vladyslav

PS And many thanks for your supplement to the initial post.

It will be very cool if you will be able to check older version for this problem and report the results. Thank you in advance.

You can try this link for testing purposes:
https://chrome.google.com/webstore/detail/tabs-outliner-main-releas/lgngaombkchpbeedhdaiglamldblanfn

it's a previous version.
but maybe it's not very good idea to continue use it for long time, as i use it for development purposes and will update eventually.

Thank you, have no access for MAC now, but I will check it. For how long do you use TO and was this problem exist for example 2 days ago? I updated a version recently, maybe it's some new bug

Cannot reproduce this problem, please report your OS and Chrome version

Actually any type of node can collect any other nodes inside. And the Ggroup is really just a fancy styled node, with box icon, you can use it for whatever purpose you like. But in case some saved tabs activated inside it then they become an active window.

Actually the update does not disable anything that was there for free. Actually it even adds more useful and free features,.... Maybe some problem arises unintentionally, but to say "many features"... HUGE problems...
Please tell us what MANY features are being disabled for you.