How to design a worm-gear in FreeCAD?
As far as I know there is not a workbench capable of producing the design you want with a single click "new worm gear".  But it is a rather simple affair to create the part you want from scratch.

What you want to do is to sweep a sketch along a helix.  It is a very similar process to the one you would follow to create a thread documented in the official tutorial (it's the "method #3" on that page).  This is how it should look like:



Since helices are subject to a few limitation in FreeCAD, I recommend to read the section called "tricks to success" and the following tips, as it is very likely you will incur in problems otherwise.