mymymy, It seems you hit the point!
Just after having rebooted Xubuntu and logged in, I launched Audacity and, voilà, I am able to select an analog output.
The analog output option is still available within the list
Even if the core reason of the issue is still unknown to me, mymymy, you made my day with your workaround!
I had the same issue recently, after using Audacity for ages without this problem. So I asked what I had been doing recently involving audio that I hadn’t done before. The only new thing was fiddling with Openshot Video Editor.
I closed Audacity and Openshot, reopened Audacity and voilà, Audacity is now back to normal!
As a double check, I started Openshot with Audacity already running. Nothing happens apparently, but if I try to change the output device in Audacity, it switches to hdmi no matter what I choose, and the application goes mad. I left it there, closed Openshot, went back to Audacity and, after a few seconds, all was back to normal.
Hope this may help to find and remove the problem.