The whole spring is forged and filed. It isn't necessary to use spring steel for this, though it results in a springier latch.
Cut a piece of metal suitable for the spring, secure it vertically in your vise with a little sticking up, and forge the head. This head does not sit at 90 degrees to the spring body, but follows the curve of the butt plate, so forging and filing will get you there.
The button's main purpose, or so it seems to me, is to cover up the rectangular slot you've cut in the butt plate. I've seen several Lehigh Valley rifles that have a very similar spring, but there is no head forged on it...just sticks out of the butt plate enough for a finger nail to flick it up.