the death korps of krieg, who resemble gas-masked wwi soldiers with a german-style helmet. purely coincidentally, they seem to be most commonly painted in feldgrau colour schemes

So they're actually a hodge-podge of the WW-1 factions.

The trench coat that the DKoK wear is basically just a French M1915 trench coat in a different colour (the original being in Horizon Blue). Note, however, that the contrast lining of the coat is German. The collar is also different from the French coat. The gas mask is based on the the Small box respirator (British) introduced in 1916, but is made in leather. The helmet is a Stalhelm with alterations. It has a decorative crest much like the French Adrian Helmet. The Puttees are clearly inspired by the British WW1 Puttees. Note that by WW2 these were no longer used. The Backpack and Pouches seem to be German. The Bayonet is German. The Shovel is most similar to the US M1910. This is because the shovel is normally depicted with a cross handle, and the US were the only ones to use a shovel with one of these. And lastly their war tactics generally don't have any set style beyond WW-1 style warfare.