I remember my dad having such a tool when I was a kid and using it to start screw holes whenever I needed to hang something in the barn. Have no idea what it was called or what it was intended to do. Here is on one fleabay. I don't remember ours being that small but maybe...
https://www.ebay.com/itm/4-1-2-Specialty-Screwdriver-with-THREADED-END/152751063512?hash=item2390ac41d8:g:VtsAAOSw7L1ZxcC N