What I wonder about from your explanation is how does a simulation know where the noise is coming from. I feeling is that inside the simulation one is unable to differentiate the source of the noise.
You're not wrong. But I suspect you'd find inconsistencies if you looked hard enough. Situations where 2 things don't interact in some obvious expected way. And that's just the simple case. If you've played enough video games, you'd know that devs can easily create scenarios where there is no way to get the correct behavior between 2 objects without doing some pretty drastic changes to their game engine. (I play a lot of simulation centric games). Basically the number of ways you can poorly implement objects interacting with one another explodes pretty quickly. So that means, that the bar is pretty high, for something living in a simulation to never notice irregularities quick enough for the simulator runner to fix them, assuming the simulator runner is able to fix them at all.
I think about this a lot, and sometimes wonder if the edges of science can't be solved until some meta being comes along and implements that edge case. And then the edge cases get weirder and weirder. But really, I'm relying on my intuition of superlinearity when I think about this stuff, and I can see certain problems with simulations going to infinity faster than, say, the infinity of the infinite time argument that we must be in a simulation.