There is a lot of information here
but it sounds like you have a "sporterized" one. It might have been sporterized in the U.S. for an American cartridge, but Austria and Germany had a lot of sports shooting and hunting and obsolete military rifles were often converted for sporting use. The set trigger was part of the conversion.
The current caliber would be anyone's guess, but mine is the 8.15 x 46R, a very popular target round in Germany and Austria. It would be smaller than the .38-56, but in the same general category. You should try to get a chamber cast (use wax for a first try) and maybe the dimensions will work out to something that is available or can be made from another cartridge.