Jan, if they say no groundsheets, and do not qualify that by saying breathable ones are ok, then it is NO groundsheets of any kind, I guess.
As for sleepig in the awning, a breathable one is no good for sleeping on as damp comes up through the holes or weave.
I think the only alternative is to have a piece of waterproof sheet which just covers the area of the sleeping unit and remove it during the daytime.