I'm not sure I follow, if I were to define "Energy System" as a system to create or utilize energy, I can think of a half dozen that never were weapons. Solar, Wind, Natural Gas, Coal, Hydro.

If you define energy systems to mean nuclear energy systems, then we only have one, which is fission.

But in the end, this test was specifically designed to test the nuclear weapons stockpile by feeding real data about implosions, by means of ablation by x-rays, back into the computer simulations that have been developed in the last couple of decades.

In review, implosion by ablation of a material by x-rays is the mechanism speculated that the primary fission nuclear device triggers the secondary fusion device in an H-bomb. So, they are not trying to figure out how to produce power or even understand fusion, but they are modeling the characteristics of a specific part of a bomb, so they can know how to test a 50 year old h-bomb without setting one off.

Interestingly, controlled nuclear fission preceded the weapons tests (Chicago Pile 1), at least chronologically.

And that's the only "energy system", that I can think of, that is also part of a weapon.