Sorry, I believe that I misunderstood your original note. I thought that you simply did not like the menu being in the "top of screen" position rather than the application's title bar (I'm with you on that) so i suggested that the double-click on the Opera side panel was at least the easy way to switch back and forth and get the menu when needed. The "O" button was there at one point but that seems to have been abandoned.
At any rate, on my system settings/appearance/behavior the "in the menu bar" & "always displayed" does at least work for Opera, but the fact that it then puts every program's menu there (that does not have a menu "button") at the screen top means that I stick with "windows title bar" & "always displayed" that and just do the double-click for Opera, for me the easiest way to toggle full screen.
On my boxes (combinations of 16.04, 18.04 Unity and Gnome) Chrome on most boxes seems to be operating like Opera with no window menu, Firebird and Chromium work just fine, Vivaldi uses a menu button. I have a few other browsers and Windows 10 but this note is far too long already..
At least I can get it title bars somewhere on them all. Bummer for you.