Modern poor countries are definitely not steam punk. You have half the population toting smart phones around and the other half collecting cow dung to cook dinner with, and a whole lot of nothing between those extremes.
The fact is, humanity's industrial rise was possible because of cheaply extractable resources. Next time around, after a collapse, then we don't get those resources again, geddit? We already grabbed almost all the cheap stuff, the remaining stuff is either far remote from large-population-supporting areas, or it's now so costly to extract that we need dedicated high-tech machinery and processes to make it cost-effective. That sort of specialized mining requires high levels of knowledge and infrastructure to maintain.
So the recovery gets up to the late medieval stage of development and then you have serious metal and fuel shortages preventing society from boostrapping another industrial revolution. In that scenario, instead of getting energy from fossil fuels, which allowed economic growth beyond feudal agriculture, you'd have to extract fuel energy from plants, which would mean diverting agricultural output into making fuels. And people would starve if you tried to do that to boostrap "industrial revolution mark 2", so society might well be stuck in late-feudal type stage for a long, long time, but with smatterings of technology that have been preserved.