If they had as little agency around the issue of population control as you suggest, this makes me question their status as "advanced."
Beyond that, if you have effectively infinite space and resources, there's no need at all to have even the slightest bit of population control. Population control is only necessary to ensure adequate resources (including space to live) for everybody. But when there's no constraint on resources, there's no reason why anybody shouldn't have as many children as they desire.
So you suggested that their civilization as a whole had little agency around population control.
Beyond that, if you have effectively infinite space and resources, there's no need at all to have even the slightest bit of population control.
You're forgetting simple geometry. Space empires can only expand proportional to n^3, while their population could potentially expand proportional to k^n. Also, in a situation where there are multiple star-faring "species," a hegemonic, exponentially expanding entity might well be viewed by others as worse than obnoxious.
Given these reasonable assumptions, it seems likely to me that most space-faring civilizations of this level of technology will never experience any kind of pressure on living space. If you've ever read the Culture series (by Iain M. Banks) then you might reasonably expect such a civilization to "Sublime" before running out of space. Or to eventually alter themselves so as to remove the desire to procreate in a deliberate move to "retire" from the galactic stage.
I said "most" because there is of course the possibility that some species comes along that has the urge not just to procreate but to have as many children as possible as fast as possible, and manages to achieve this level of technology without ever altering this behavior. Such a species that is driven to expand its population as fast as possible may then experience restrictions on living space, but such a species would eventually have to enact population control, which could take the form of altering themselves to remove this urge to procreate as fast as possible and therefore will become just like "most space-faring civilizations".
From the POV of an outsider or a different species, would any entity care about the difference between "effectively/pretty much" and what you deem to be "actual" population control?
I doubt it.
So basically, you haven't been disagreeing with me, just splitting hairs on what the words "population control" means. I'm using a more generic criteria: Is the population controlled?
As I understand it, the argument is basically that, assuming true high-fidelity virtual reality is possible, then it's likely that any society that advances far enough technologically will eventually create a virtual world and populate it (or let it populate itself) with virtual beings that don't know they're in a virtual reality. Given this assumption, if you let the virtual reality run long enough, then the virtual beings inside the virtual reality will eventually end up creating yet another layer of virtual reality. Assuming this is possible at all, it then follows that there could be an effectively infinite number of virtual realities layered inside each other, and under those circumstances, it's extremely unlikely that our reality happens to be the outermost "real" reality but is instead somewhere in the stack of virtual realities.
1. Advanced societies have probably solved the aging problem, leading to either extremely long lives or effective immortality. As long as these societies keep reproducing (and they will, unless they deliberately engineer out the urge to procreate, which I consider to be unlikely), they'll need space to spread out. Sure, they could probably pack themselves like sardines into a single solar system, but that only works if they'll be spending 100% of their time in virtual reality, and that would be begging the question.
2. A need for resources. Type III societies can capture 100% of the output of a star, but even this amount of energy might not suffice once society grows large enough. And even at that level it's still probably easier to manipulate matter than it is to convert energy into matter, so it'll be more efficient to harvest planets and asteroids and whatnot for raw building materials, which means leaving the solar system.
3. Even assuming they manage to create virtual reality that is 100% indistinguishable from reality, it's likely that there will still be a lot of beings that will reject the idea of living 100% in virtual reality simply because it's virtual. Even if it's indistinguishable from reality, they'll still know it's not real. So they may visit VR, but will want to actually live in the real world. Or in other words, humans have shown a tendency towards the perverse, and it's not unreasonable to assume aliens will too.
4. Any kind of scientific research still being done at that level will likely require the use of reality instead of VR. VR is a simulation, and even if it's indistinguishable from reality to your senses, it's still presumably not actually simulating reality down to the planck level (because it's part of the universe, it cannot simulate the entire universe at the same fidelity that the universe itself operates at, as that would presumably require more information than the universe contains), and so there's probably a fair amount of research at that level that simply can't work in simulation and requires testing against actual reality.