You seem to know
No, I don't, since I have not done any test myself and have not read any studies on this matter.
Do you think that forged clubs are "softer" than cast clubs?
I don't think, I KNOW that forged clubs are softer. I've taken Material Science Engineering courses, and I know the basics of steel manufacturing.
Is the steel in forged clubs different than cast clubs? If so, is it "softer"?
Yes, steel used in forged clubs are softer, otherwise it would be more difficult to manufacture them.
Do you think that an impact into something softer gives off more or less vibration than an impact into something harder?
Yes, the vibrations would be different. But there are other factors in play.
First, the shape has probably greater effect on vibration differences than the softness of the steel.
Second, as I have said again and again, just because there is difference, does not mean that you can "feel" the difference, especially without sound. The study is saying that if you take a forged club with a shape that will create harsher sound, it is going to feel harder than a cast club with sound dampner that will give it a more pleasing sound.