This is a very interesting discussion! I'll chime in with my thoughts.
I'll start by saying it's hard to define a term that only exists within a niche community because it is colloquial so there is no official definition AFAIK, but the effort to come up with one might be a good exercise.
I've always thought of the term "sabersmith" as an analog to "blacksmith" or "bladesmith". In both of those cases, the smith begins with the raw materials, usually high-carbon steel or some other metal, maybe some wood or leather, melts it down, cuts it, shapes it, and forges those things into something. I associate it with starting with very little and applying a high level of physical effort to create something amazing. So, with that in mind, I have always thought that at least some level of fabrication (machining, cutting, bending, etc.) as a requirement.
So, to me, it has to be something more than simply putting parts together. I'd say the term "installer" is more accurate in that case; It's not creating something totally new from materials, it's just putting together things that somebody else made. There can be joy in that, and a good installer is to be respected because, well, nobody wants a bad install! It's just not "smithing", IMO.
I also feel like "sabersmith" should be reserved for those with expertise in metalwork that create unique hilts of their own design or based on what they've seen on screen as closely as they can manage.
To follow up on jbkuma's earlier comment about code work possibly being considered, I think there needs to be a separate term to describe those who build and develop their own saber control systems or advance existing open source solutions. This is a more recent development that it's become widespread enough to talk about, but I'd like to coin the phrase "saber engineering" to describe that kind of thing. The skill set required work on the code and the intricate electronic inner-workings of a saber differs greatly from working metal to form a hilt.
"Smithing" to me seems focused on the physical outward appearance and function of the saber, while "engineering" is focused on the inner-workings and behavior of the saber; how it all works. Both are needed for a good saber.