@vascopj The whole point of private browsing is that no one can recover your browser session and view the history of that.
In private the visited pages aren't saved anywhere by Opera, so there's no way to recover that.
Like you found, checking your OS's (Win 10) recent DNS cache might give someone a clue as to what recent sites you've visited (in private or not) but it's never going to give you back your actual browser private history, just the recently cached DNS domains.
I've had 100+ private tabs window sessions that I've lot due to Win10 deciding to update when I wasn't expecting, so I know how annoying it is. But the only thing you can do it try to prevent it: one way is to postpone Windows Update (and auto restarts/reboots) far into the future or to just turn off Windows Updates. Neither option is ideal, since one should keep Windows updated with the latest security updates. Note this won't prevent reboots due to power failures, etc.
Another trick I've done before to prevent losing private history if I know I need to restart very soon is to save the whole private window as a bookmark folder (via Ctrl + SHIFT+ D), doing the restart, and then re-opening all the tabs from that Bookmarks folder and then deleting the folder.