Do spoke nipples come in one standard body size for the gauge?
Here's measurements from 3 in my immediate vicinity:

Sapim Sil Brass 14G 12mm, I believe featuring the Sapim Polyax design: 3.7mm

Wheelsmith Duristan BN14 (Silver 14g Brass): 3.82mm

DT Sil Brass 14g (I think): 3.9mm

(I don't have al nipples to measure at home, sorry.)

That's more variance than I would have expected.

One major point of design consideration for this area of the nipple (the round part and the shoulder) has to do with different manufacturers' schemes to get the nipple to swivel as freely as possible in the rim at whatever angle the design of the wheel puts it at, to avoid bowing of the spoke due which can lead to failure, or to avoid having to take steps in wheelbuilding to correct the spoke line at the nipple (the Bicycle Wheel by Jobst Brandt has more info on this). I imagine you get more swivel the thinner you make the round part, but the tradeoff is you want material there behind the threads to avoid failure, especially with an aluminum nipple.

Sapim emphasizes the swivel factor with their nipples so that might explain why their number is the smallest of the above.

A related note is that the outside diameter of the area in question doesn't really vary much between gauges. That's one reason why many prefer 1.8mm threaded-end spokes (either straight gauge or Supercomps) for disc brake wheels with al nipples - you get more material there to counteract the extra stress of the brake, which can contribute to nipple breakage.