I'm sorry for resurrecting a 3 year old thread, but I thought this was worth it.
I ran into the exact issue as the original poster. It's still not possible to move the mixer to a virtual desktop, because it's not a separate application, as far as the OS is concerned. Then I realized that Presonus already offers something that's the perfect workaround, Studio One Remote.
https://legacy.presonus.com/products/Studio-One-Remote
Studio One Remote works over your network, but surprisingly, also works locally. Works on MacOS and Windows. Launch Studio One, load your project, then in the virtual desktop, launch Studio One Remote, your local session will appear, just click it and load the mixer. The Remote app is pretty lightweight, so there's really no performance penalty running it this way.
Just thought I'd share.