is it common not to have wood under the stucco on walls on a new home ??
Original three coat stucco used a 17-ga or 18-ga wire in a hexagonal mesh similar to chicken wire. Over-lapping horizontal layers of black tar paper would be attached to the studs or to sheathing and the wire mesh fastened to the studs and sheathing through the tar paper.

https://www.youtube.com/watch?v=ihp0QaUZc18

https://www.youtube.com/watch?v=qqYgqbiwqNs

https://www.youtube.com/watch?v=PQ5N69SoAJE

A house now under construction in my neighborhood was entirely sheathed in green ZIP OSB. Part of the exterior is stucco. The installers put black felt over the ZIP board and then nailed a metal mesh different from the original type over that. I assume they nailed into the studs and in between. I saw them apply the first coat. I don't know how many coats are used in this application, but I suspect it is only two.