A question one might be inclined to ask is, what are the largest countries in Matthew White's world of 2900, the New Middle Ages, and are any American states up there?
First, let's largely make the assumption the outside of America, and above the 10th parallel, are pretty close to the population of the Old Middle Ages. We can see the biggest nation states at the the beginning of the second millennium, as well as those as the Middle Ages came to a close, and there does appear to be a recurring consistency; We can largely bank on the ruling Chinese dynasty, a Muslim empire or two, a sizeable chunk of India, Japan and France. The Byzantines, Holy Roman Empire, Inca or Ottomans would require some contrivance to bring back, but it's reasonable that we could see some successor states in the mix. The only region of North America that would stand a chance would be Ohio, which at between 8 and 9 million. It's definitely reasonable to suspect it could place in the top ten, but it's no guarantee.For the most part, the major population anchors have been consistent throughout history, and it was the Age of Exploration, and then the Industrial Revolution, .created new major masses of society in America, Brazil, and Sub-Saharan Africa (and actually a major extension in Russia). It's probable that the extreme climates and lack of navigable waters could see the populations crunch more than they would in America, though all three have at one point seen sizeable empires pre-Industrialization. (For it's part, Russia would be the only "old world" polity where its population could be twice the size of what it was in the Old Middle Ages)
Actually, another thought experiment might be "2900 population with contemporary borders". Interestingly, the top three would very likely be the top three we have right now. (A "right now" that has been the case for a couple of decades, but is rather temporary) The lowest estimates for China is something like 60 million, and it is believed that it could have been as high as 100 million--and that's covering less territory than it does today. The Indian subcontinent is also believed to have contained roughly 100 million people--current national lines would cut out countries like Pakistan, Bangladesh, etc, but that would still put it up there. And the U.S. of course canonically has 57-58 million people. One might reasonably switch these three around, but logically these would be the firm top three.
There would probably be a major gap between these three and the next major borders--Indonesia is the fourth largest in contemporary times, but the island of Java (where more than half its people live) in pre-industrial society would normally top out at 4 million. I've seen figures that range from six to ten million, so it wouldn't be unfair to go with the high end. Nigeria, Japan, France, and Germany are all estimated to have a low eight figures. Slicing off the part of the Indian subcontinent that makes up Pakistan would probably make it sizeable in its own right (Giving it France's population density would handily make it the fourth most populous at 22 million, That being said, in proportion to the collective population of the Indian Subcontinent, it would probably be much less, probably 12 million), but I don't have exact estimates. Rounding out the "original" would be Mexico, which is was estimated to have something like 15-20 million, and unlike the Andean states, wasn't carved up.
As for Colonial/Settlement nations? Well, White doesn't give us any information except for the U.S. and Canada. I've mentioned this before, but using a tactic of reducing a country by is urban proportion, adding its 1900 population, than dividing by two gives us White's figures for the Eastern U.S., Canada, and correlates with the estimates of Pre-Columbian civilization. I've therefore applied to the rest of the New World, and this would give Brazil 20 million people--leading contender for the fourth most populous. Also, another country I'm treating like a "settle nation" is South Africa. It has a lot of the qualities of places like Canada, Australia, and the Southern Cone; Geographically large, fertile and relatively temperate lands which were under a million before the Industrial Revolution, and settled largely by White Europeans. However, its Afrikaner past might not be reflected in the New Middle Ages. Unlike those other places, Whites never mad a majority, and don't even particularly have a large congruous landmass. The probably ten million of South Africa would largely resemble an extension of the African civilizations of the north. And speaking of such strange Old World hybrids, there's Russia. Russia very much orchestrated a settlement into Siberia, and some 38 million live there now. Applying the same crunch as Canada would still give it something like four or five million. This table of historical populations consider trans/intercontinental countries known as the Commonwealth of Independent States distinct from both Europe and Asia, and for the purposes of the New Middle Ages, we probably should too. I generally want to minimize the difference between the Old Middle Ages and the New Middle Ages outside of America itself, but I think a Muscovite Russia extending into Siberia (and the occasional migration of Central and East Asian peoples) could still be something in excess of ten million. (Of course, there's always a possibility of steppe tribes just wreaking havoc and bringing everything back to factory settings.
But one could ultimately make the order 1) China, 2) India, 3) USA, 4) Brazil, 5) Mexico, 6) France, 7) Russia, 8) Japan, 9) Indonesia and 10) Either Nigeria or South Africa (and have one of those plus Pakistan to round out the top 12) for a somewhat balanced, historically accurate and consistent world-building. Of course, actually, the top five is very "Americas" heavy, (This is largely due to New World nations generally being geographically bigger), but this is definitely what I think the top twelve most populated areas on the Globe, in the White's 2900 would be.