When I have a sketch arrangement (multiple instruments, effects, motions) in Scaler 3, how do I copy the entire session into a DAW (in my case, either Studio One or Ableton)?
As I know, this is not possible because you cannot copy the instruments nor effects. You can only drag/drop your chords and motions (if you used them on the Arrange page) by lassoing the entire content of the Arrange page.
But, there is even better way to do something similar to your idea.
You can route the tracks on the arrange page to the track in your DAW. I don’t use either of your DAWs, so I recommend you do check in Scaler 3 documentation. Click on Scaler logo, select Help section and there is a button Open Manual. On the page 75 you’ll find section Arrange Page > Multi-Channel MIDI Out and near the end of the page, after the explanation what External MIDI output and MIDI Output Channel are, there is a link to a document that explains routing in several DAWs, including Ableton and Studio One.
In your DAW, you can add instruments and effects as you usually do.