The solution let itself be known. Opera in "Full Screen" is different than an individual page in full screen. The menu bar at the top disappears and there is no pathway back to other applications, let alone other open windows in Opera.
I don't know which version of macOS you use, but as far as I can see every application on macOS works exactly like that. The menu bar is 'floating', you can make it reappear by hovering your mouse at the top of the screen. You can use the menu to switch to different windows. The same is true for the dock, it appears when you hover your mouse at the bottom of the screen, and it offers a path back to other applications.