The sterling or coin silver just turns black after a while. Even 'Fine' Silver will oxidize a bit.

Alot of the guns from Kurt Jeagers shop after the war seem to have had silver inlays. Perhaps there was a problem getting gold suitable for the inlay work,,jewelry alloys are generally in the 10,12,14k range and the lower karats can be difficult to work. Coin silver or sterling works pretty easily and was fairly plentiful. Just a guess.
At any rate, it does oxidize rather quickly to a fairly tough matt black surface.

They could be steel inlays, but I'd expect them to have the same bright blue as the other blued parts. At least the same blue color as the spliced in part on the top tang. Using something like 12L14 (ledloy)steel today, steel inlays are not much of a problem,,certainly not much more than working with 10K or 12k gold. That can give you a fight as it work hardens so fast trying to get it set.

Some Ithaca higher grade SxS's had the inlays done in silver and are often mistaken as a steel cut figure instead of the silver they are for the same reason.