I find these questions about the "current state" of old papers confusing because such questions about "current state" seem to assume that the validity of papers is changing like the weather. Well, it's not. The current state of the Katz-Vafa papers is that they are correct and important papers on F-theory that are almost 15 years old. It's very likely that they will always be correct and important papers from the late mid 1990s.
On the other hand, the recent (five years or so) F-theoretical bottom-up phenomenology by Vafa, Heckman, and others (let me mention Marsano, Saulina, Schafer-Nameki, Dolan, Wecht, Cecotti, Cheng, Seo, Kane) is still a relatively new research direction that continues to be very active. It sometimes uses older papers such as the Katz-Vafa ones but it is surely not "just about them". The newer work is focusing much more on the physics of singular cycles and phenomenological applications, among other things.
The particular questions raised by the papers in the mid 1990s have been largely answered so there's not too much room for completely new fundamental research; however, that doesn't mean that you can't discover something completely new over there. The F-theory bottom-up phenomenology remains full of open questions and it's surely an excellent area of research if someone can get familiar with everything he needs. This F-theory phenomenology has become one of the 5-6 major "scenarios" how string theory could be realized in the real world.