In private window, page icons (favicons) are replaced with incognito icons. It's a remnant of an old Opera 12, where private tabs were in the same window as the normal tabs, so marking private tabs with separate icon helped distinguish them.
In the new Opera, it doesn't make sense to mark each private tab as private, because private tabs can only exist within separate (private) window. In this case, it is enough to mark only the window as private - which is already done by different address bar/window color.
Please consider removing this icon replacement. Removed page icons really make browsing difficult, especially when working with many tabs. Opera is the only browser with this pointless 'feature'.