That is a Greist screwdriver - it is not like what came standard in the Singer sets. Simanco screwdrivers do not have that collar on them. I have a lot of Singer manuals, and have not seen one that shows that style screwdriver. I also have several Greist attachment manuals, and that is what they show.
Since Greist also sold aftermarket attachments that fit Singer machines (along with a whole bunch of others) - finding it with Singers is no surprise.