Since this inconsistency with the correct functionality of the history was never corrected, and another issue was the identical appearance between the window mode in normal browsing and the window in private browsing, I decided to completely remove Opera One and migrate entirely to Opera GX, also in standalone (portable) mode.
Opera GX does not exhibit the declining aspects of Opera One, such as the reported bug in standalone installations where the browsing history doesn't work correctly, and it does show a distinct browsing appearance between the window in normal mode and the window in private mode.