"Still separate countries with separate armories and production."
The point is that they weren't until 1919.
Hungary wasn't created out of the old A-H empire and didn't fall into existence with brand new firearms for its military, in a new chambering.
They used what they had access to, and what they had access to in 1919 were MILLIONS of Steyr straight pull rifles left over from the Empire.
Even well into the 1930s, during the depression, there wasn't a huge amount of money to be had for rearming, so the old 8x50R rifles from the empire stuck around.
Austria and Hungary maintained close ties in the 1930s, and both adopted, and manufactured, the 8x56R round that was developed in Austria by Slothurn.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.