Interesting - I reinstalled a previous version (I really don't know which version I had - but I never had received a notification to update before), and it is doing the same thing. No matter what desktop I switch to, the OBS program is showing up. There must be a setting somewhere that I am missing. I used to be able to keep it on desktop four or five, and record anything on desktops one, two, three without having it record itself (and that amazing prism).
I have found a work-around. If I make OBS full-screen I can go to the other pages with no effect. So, I guess it "works", it just doesn't work like it did - and I think I must have inadvertently selected something that makes OBS visible on all desktops.