New Orleans finish
I live in New Orleans. I was wondering what tool was used to finish the stucco on the old buildings. The finish is very flat and almost smooth.

The tool they used was a cork float. I still have my cork float, although I haven't used it in years. It is way too slow
The reason I know is I have been to your fine city twice for the Mardi Gras, and was amazed at the quality of the stucco on the old buildings.
Years ago, here in Virginia, cork floats were used by plasterers to float cement basecoats. This process was slow but provided a very dense, crack resistant basecoat.
If you happen to use a cork float, never let it soak in a bucket of water. The glue will dissolve and they fall apart. If they are kept clean they last a long time.
Somewhere in history, our forefathers decided cork was an ideal material to float stucco with. Cork is great, but way too slow.