TL;DR: Umami is kind of like, the idea of "savory." Parmigiano Reggiano, anchovies, mushrooms, lamb, and marmite. None of those things taste alike yet they all contribute an element of "umami" much in the same way that vinegar, lime, and tamarind, etc. will contribute sourness while tasting nothing alike.
Personally, I think the ostiole end of some Black Missions have an umami thing going on that's sorta in the family of parmigiano reggiano in terms of flavor profile. I definitely see how umami can be applied to figs; kind of sweet and umami in varying proportions.