https://www.geeksinphoenix.com/blog/post/2017/02/28/how-to-setup-family-safety-for-windows-10-using-microsoft-accounts.aspx

and scroll down to - just past the halfway point or so..

and ya will see this heading called - Web browsing

as ya read this - windows 10 needed an update..so prolly win 8.1 needed it too..

The update was around 11/2016

so perhaps ya did not get that update..

but sounds like ya already have it.. *just a thought..

n e ways here is what update does or not lol

(the search thingy is turned on and InPrivate browsing is turned off)..

may be a way around it.. if ya read.. *not sure tho..

the read also may help if a browser is blocked.. *just another thought..

I can run private window under Firefox. It's work sucessful.

Firefox isn't Chromium-based like Opera. It's best to compare with other Chromium-based browsers like Chrome, Brave and Vivaldi.

Reinstall opera can't resolve problem.

Did you also choose to delete your data when you uninstalled Opera? If not, and the problem is in your Opera profile, uninstalling and reinstalling Opera won't help. If you don't have anything to save, uninstall Opera again and choose not to keep your data. Then reinstall Opera.

Do you have any extensions installed? If so, disable them to see if one is causing the problem.

family safe account

Can you test Chrome under the account to see if it has the same problem?

Opera doesn't support Chrome policies, so it can't be https://geekermag.com/disable-incognito-mode-chrome-windows-10/.