In short, just because we're in a mathematical construct doesn't mean that we're not part of a simulation within that mathematical construct. Simulation argument and the universe being a mathematical construct are not mutually exclusive.

Sure, but if anything it seems like they both apply - we are overwhelmingly likely to be simulated humans in a mathematical-construct universe.

Why would you even need that much? If we're just talking about the mathematical idea of this universe, it exists whether or not we know how to define it. It's not inconsistent to say that someone defining but not necessarily calculating the math is the necessary and sufficient condition for us to experience it, but I don't see why you'd draw the line there.

I was trying to make it clear where the tradeoff with mathematical Platonism is. If you believe mathematical things exist eternally, or exist when defined, or exist when explicitly calculated, that affects what limit you have to place on human civilization's achievements (and if you're a straight-up Platonist then you can't make this objection at all, because as you say, the idea of the universe already exists).