Very good tl;dr apart for a detail: it's not about the complexity of a single simulation, it's about the ratio of complexity of two simulations. In this way we can factor out our ignorance of the details (are we a brain-in-a-vat? Is the simulation run on an abacus? Is it written in Phyton?) and clearly establish which simulation is more complex.

Now, since by a counting argument we are more likely to be in a simple simulation, by looking at "optional" complexity around us we can establish if we are in a simulation. Reaching 5 sigma of confidence should be enough, so if we find out that the universe could have been 10 million times easier than what we experience, then we can be pretty confident that we are not sims (I assumed a linear scaling of the simplicity assumption here).

Now the tricky question is, which complexity is "optional"? I would argue open space which we would probe if we do interstellar travel, but maybe there are better ways to find optional complexity.