Square shank press-fit extensions are shown in four catalogs (1925, 1928, 1932, 1933) for 3/4-inch drive. For some reason, they held on to them longer in the Heavy Duty socket sets. They're shown in two catalogs (1925, 1928) for 1/2-inch drive. The 1932 catalog, which is the one with all the new numerical model numbers and the parenthetical notices about the old model numbers, shows rounds shanks with male and female connections forged onto the ends, listing them as "5461 (Old Part No. DE5)" and 5463 (Old Part No. DE10)" respectively. DE5 and DE10 are the square shank press-fits.
I have never seen one, either, in the wild or photos. But I've only seen a few examples of the early 'phonetic era' pieces, which are very scarce, right here on GJ, and those were a few at a time, and then Oldtuleguy's partial Y set. I'm not saying the catalogs prove they made them. But I am saying it doesn't seem likely they used that specific image that many times over the span of several years in several catalogs, then carefully noted their replacement, if they didn't make them.
(Didn't mean to break into a Plomb conversation on the MTF thread!)