It was generally leather rather than webbing, though I have seen a few pictures where webbing shoulder straps are attached to the leather belt (I think those are part of the late-war backpack when leather was getting scarce).
I may be wrong but I don't think either the Germans or Austrians had the Y arrangement at this time (or if they did it was uncommon, like in the different equipment ski troops had for example). I believe any shoulder straps you see are part of the backpack arrangement. Almost always on photos when there is no backpack there are no shoulder straps.