I had a 12ga Walther SxS a few years back.
About the same description of yours otherwise.
I think mine was 1937 mfg/proof, but I can't swear to it.

The insides remind me of the Walther P38 in that there are a lot of stamped parts, coil and torsion wire springs.
Probably a bold jump from the standard German SxS builds of the time.
The trigger guard and safety button are Bakelite or a similar product. Might be the same as the P38 grips?
When you take the trigger guard off, you can see the cast -in-place sheet metal reinforcement piece inside it on the front end .

I have a Walther catalog reprint from the period and they are in there. IIRC there were a few different versions all built on the same basic gun.
They even listed a simple one standing leaf 'rifle' style rear sight dovetailed into the rib. No rifle bbl'd guns that I remember,,just for better accuracy shooting Brenneke's I guess!