Warren in Lancaster, PA
I have a 2 3/8 dogwood bench screw that was cut in a screw box. Screws made this way have a somewhat smoother surface, but the box and tap cost over 1000 euros. Screw boxes like this are illustrated in Plumier (1701) plate 55 and Roubo (1769) plate 311.

The Dominy tool collection has a screw box and two taps, a smaller metal tap and a larger diameter wooden tap. There were probably other tools in this set that are now missing.

Richard Starr wrote a long article in Fine Woodworking around 1978 detailing how to make wooden screw boxes and wooden taps. I think this article did not make it into the digital publishing of old magazines, unfortunately.

Large screws like for cider presses were 9-12" in diameter; I think they would have had to have been carved. I don't know how they made large nuts for these.