Wouldn knowing the detailed chemical composition of a star be better than just the mass to determine the fate of a star?
Chemical composition does matter somewhat- for instance if a star were to start out with an unusually large amount of carbon or other heavy element, that might change the star’s subsequent evolution. However stars are composed overwhelmingly of hydrogen and helium, and it’s primarily the total mass that dictates the evolution, since that’s what determines the balance between gravitational and thermal pressure; differences in chemical composition are a pretty small effect compared to that. (A thing that’s more likely to change a star’s evolution is the presence of a binary companion. A nearby star can exchange matter with its neighbor, and change its evolution, often quite dramatically).