Before we get all excited about sources of energy it’s important to recognize that Kardashev’s idea was a product of its time and circumstance. Soviet central planning clung to primitive assumptions (one of the many reasons the USSR collapsed in the end), one of which is that energy use per unit of output is essentially invariant.
This is, of course, wildly untrue. A US clunker from Chrysler, Ford, or GM back in the early 1960s could consume a US gallon every seven miles; today we expect automobiles of the equivalent interior capacity to consume a US gallon every 20 to 50 miles. Likewise the energy required to manufacture consumer goods, industrial equipment, etc. has also fallen dramatically due to “learning curve” effects. Furthermore, as the population stabilizes and then falls, total energy requirements for any given level of per capita consumption will likewise fall even without learning curve efficiencies.
In short, there are so many flaws in Kardashev’s argument that it’s utterly worthless using math to extrapolate into the distant (or even near-) future. As we all should try to remember: when your fundamental assumption is wrong, everything thereafter is “wronger and wronger.”