I just tested this - the Apple Pencil does work to input notes in Sidecar on the iPad; I’m running the latest updates for both mac and iPad. Pretty cool!
I don’t think you can separate the low zone into a floating window, but you can use two separate windows, one on the Mac and one on the iPad, and minimize the lower zone on your main display’s window.
Maybe you can keep the lower zone closed in the Write window (main screen). And then open a second window (maybe in Play mode), and move it to the iPad.
I detail my experience using the Dorico lower zone in a separate window on a separate display in Windows. I found a lot of issues, including that it enters wrong notes on the main window while sounding them correctly. I’m guessing this is a hangover from the move to iPad which doesn’t support multiple windows. Except the special case you mention here which is side car. Daniel mentioned this use case to me last summer so I’m sure it’s meant to be supported, but is part of the cleanup that needs to happen with Play and the lower zone.
Anyhow keep an eye out, I found that this application isn’t ready for prime time yet.