@leocg
Solved!
When looking at your screenshot I saw that the "+" button to add tabs did not appear, and that the bar with the login, configuration and Share buttons was at the bottom of my screen. That gave me the clue that it was a design issue. I went to Settings and Design, and there I saw that the Create tabs option was disabled.
@leocg There is if you are willing to go to the trouble of actually closing Opera rather than using your device's Back button or merely switching apps. Also there is a setting to dismiss open tabs after 2 hours. I've trained myself to closing the browser, using the Close button on the top of the menu, which also means I don't see any annoying notifications when I'm not using Opera. And if I do want to come back to a tab, I use one of the other methods to dismiss it.
But then again it's akin to general Android-11 and on the earlier versions of Opera (pre-80) files could be downloaded - at least to the internal storage-space. External SD-card has always been a problem with Android-11-TV-edition - which is not Opera's fault. But it would be nice if at least the internal-location-download could be re-established again so that downloads would be possible AT ALL as they've already been in the past.