I don't think it is infinite - each universe can only have that mass/energy that fell into the outer black hole in the parent universe. At some level you'll inevitably have black holes with universes that do not have enough mass to form another inner black hole.
Unless, although there's no reason to currently believe this, the energy requirements for physics are relative within each black hole, sort of (but not strictly) like how the speed of light is relative for all observers. And we can get a little crazier, and imagine a meta universe that is sort of like a Klein bottle in that it doesn't just recurse all the way down but somehow folds back into itself. Again, no current reason to believe anything like this but it's a mind-boggling to visualize.
How much mass is required to form a black hole in a new universe with perhaps different physical constants? It could be that 'ability to make black holes' is a prerequisite for successful universes in the way way that good genes are a prerequisite for successful organisms. The universes that fail to spawn black holes are 'dead ends' so any life is statistically likely to find itself in a black hole spawning universe.
Maybe there is an 'incentive' for universes to form with physical constants tuned to produce black holes with the available energy in that universe.
The trick is that bigger black holes are less dense. Supermassive black holes can have the density of water. If the universe is gravitationally closed, it would have the density of... well, just look up at night. (Actually much less than that; you see more stars because you're inside a galaxy.)
The density makes the scale recursion less mysterious.
That’s interesting! When you are referring to density, are you referring to average density within the event horizon? Isn’t most (effectively all) matter concentrated in the singularity? Would love to hear you elaborate on this thought further.
We can't really talk about what's inside a black hole. From outside, it has a volume and a mass, and that's all there is to know.
We can say that any particle inside the horizon is inevitably headed to the center. (That's why we can't say any more: no other information can escape.) That does lead to a problem in that all of the mass would be concentrated at a single point at the center, whose density is division-by-zero.
But I wouldn't put too much weight on that. We already know from quantum mechanics that there isn't really any such thing as a "point". The math is still a problem, but the solution almost certainly lies in that direction.
