How old of POD? I'd argue the easiest is the Yuan Dynasty since they controlled most of that area anyway, at least nominally. Toghon Temur was fairly effective at fixing the problems that plagued the Yuan in the 1320s and early 1330s--unfortunately, he had the terrible luck of natural disasters and lost a few important battles against the Red Turbans that spiraled into complete disaster. If we presume he does a little better and surpresses the Red Turbans, then his two sons Biligtu and Uskhal (both of whom were extremely potent foes to the Ming, especially the former) could likewise do a good job solving Yuan's problems, although Uskhal might only live until the mid-1390s given the age his father Toghon died at.
Regardless, those three khagans (and let's assume maybe 2-3 other competent khagans in the 15th century) could prolong the Yuan's survival until the mid-late 16th century or maybe into the 17th century. In that time, it will be very much a Sinicised dynasty and a lot of Koreans and Chinese will settle there. Bonus points if some khagan takes another swing at Japan (maybe one of the Ashikaga shoguns aka "Kings of Japan" requests it and the wokou are proving especially irritation so the Yuan court spins it into something bigger) and decides a dual north-south invasion using the more developed Manchuria (including Sakhalin) as a springboard--I can only think that's a fantastic way to get the Yuan more focused on the north and Kublai Khan desired it until his death and only begrudgingly accepted his ministers's advice not to. Similarly, the descendents of Genghis Khan's brothers, who had fiefs in Manchuria and Inner Mongolia, could increasingly Sinicise themselves. I don't think it's possible (or desirable) for the Yuan to mess with them since it was basically illegal under dynastic law and their OTL revolt under Prince Nayan devastated the area which is the opposite of what we want. We'll also assume that the other Mongol khanates like the Chaghatai and Jochids do no better than OTL.
So when Yuan collapses, any Jurchen or Mongol state is too weak to reassert regional power (and might be mutually at odds) and the real power in the area are Han Chinese and Koreans (perhaps Sinicised Koreans) and the area falls into the hands of the successor dynasty. This successor dynasty never gets as conservative as Ming did and still remains fairly open. The settlement of the area continues, both officially and unofficially, since some ministers might notice that having a bunch of ethnic Han settlers in the area acts as a good hedge against the barbarians since there would be few or no attacks on northern China. Crushing the khanates in the west (Borjigin remnants and others) would also be a security measure and they could do something like the Dzunghar genocide for the same reason and acquire the borders OP specifies. We'll stop the scenario here and imagine this dynasty successfully limps its way to the modern age and reforms into a nation roughly as bureacratic and economically developed as modern China (still too conservative for quick economic development, but no deep pits to pull itself out of caused by the Warlord Era, Japanese invasion, and Maoist mismanagement).
If we're going to assume a 19th century POD, then I just don't think it's feasible since the Qing were pretty poor off in that era and can't easily block Russian expansion into that region without European aid, except Russia's main enemy Britain would prefer Russia wastes time and resources there instead of expanding into the Balkans or Central Asia.
So overall we could probably have significant settlement in those regions with a Chinese mindset like this and internal incentives. But I think the most distant regions will be inherently less settled, like for instance the shores of Lake Balkhash will be difficult to draw settlers to because of how remote they are and how Xinjiang is still not "filled up", so reaching Xinjiang's population density and resulting population (14.5 million) would be challenging. Outer Manchuria and Sakhalin have the problem of terrain--the seas around both freeze up in the winter and Outer Manchuria is extremely mountainous and only a few areas of good soil unlike the rest of Manchuria which has good farmland and very good soil. I doubt more than 20 million in that region. The area around Lake Baikal is very good for agriculture, although has many mountains, but access is difficult because one must pass through the Gobi Desert and nearby mountains to get there, so early settlement (which is crucial for high population density come modernity) is difficult at best. Maybe 15 million at most in the 1.5 million km2 surrounding it.
OP is incorrect that Yakutia has good soil--it does not since the chernozem belt that stretches east from Ukraine does not extend much further north than Baikal. There is a reason why the Russians settled Siberia the way they did, after all. While agriculture has been done in Yakutia since the 19th century (long daylight and warm summers helps, but the potential for early or late frosts is damaging), it seems to be fairly marginal at best and nowadays mostly limited to vegetables and gardens. It's also expensive to develop since it has high heating requirements (as it is the coldest place on Earth outside of Antarctica) and the permafrost requires very specific and expensive methods of building. So I doubt you'd get much more than 8-10 million in the entire stretch from the Lower Yenisei to the Kolyma to the Bering Strait, probably about half in Kamchatka which is a good place for an airport/seaport (northern great circle to the American West Coast) and has very good and mostly volcanic soils. At least if Kamchatka is settled early enough.
There is also a core population restriction of protein. The Chinese desire a high meat diet because it is prestigious and signifies wealth. Modern China is only about 75-80% self-sufficient in meat and this is by far China's largest food import (China is self-sufficient in grains and in recent years was the 6th largest exporter of rice). I suspect these marginal areas, some of which have very good soil for herding or growing crops for animal feed, economic logic will prefer this region be converted into pasture which is going to be less dense than a patchwork of farming towns so encourages migration to cities. These cities might be not even be in the region but larger cities in China proper, especially since local cities have unpleasant climate (too cold) and may be based on boom-bust industries like regional mining.
It goes without saying that this China would be a global superpower, and one probably less dependent on outside nations than modern China is. However, as noted it would still need to import a lot of food (meat) and the modern paradigm of global trade does mean it's cheaper (and beneficial to Chinese hegemony) to invest and import from foreign mines than develop yet more mines in Siberia.
What do you think? Would it be possible to prevent Chinese emigration to Southeast Asia and California, and later the one-child policy, with this program? How powerful would be this such Chinese monster stretching up to Arctic?
There's too much corruption baked into the Imperial Chinese system to prevent a significant amount of emigration, and too many countries in the New World who couldn't be convinced (or lacked the capability) to ban Chinese immigration. For instance, Chinese kept coming into the US after the Chinese Exclusion Act because they would go through Canada (slightly less restrictive) or especially Mexico (no restrictions at all). Back in that era, it was common--and well-known to the authorities--that the Chinese would just walk across the border and if anyone asked they'd claim to be Mexicans.
Manchuria and Hokkaido only settled in 19th century, so you have extremely narrow time window. I think number would be very limited.
Thing is settlement in Manchuria was deliberately restricted by the Qing. During the Yuan dynasty at least it had ethnic Han settlement, even if most of the outside settlement were Koreans (who fled, perished, or assimilated because of harsh winters, epidemic, and above all, the decades of war in the region because of the Red Turban Rebellion and Ming-Northern Yuan wars). Incidentally, Outer Manchuria is extremely agriculturally productive for wheat, barley, vegetables, etc.
Hokkaido was similar anyway in that it was off-limits to settle (outside of the southern Oshima Peninsula) since its feudal rulers preferred making it an extractive colony for furs, fish, and strictly controlled trade with the Ainu. I'd argue that if the Chinese ever controlled Hokkaido (extreme difficulties of that aside unless we're talking Tang Dynasty or earlier POD), they'd probably act similarly because it's a distant region for extraction and would let them do backdoor trade with Japan (kind of like how Sakhalin was used OTL).
Well outer Mongolia only has 3 million people OTL so 20 seems unlikely and the lake baikal region has 1.5 million (if we're being generous) so 50 seems very unlikely
In the case of the former, a huge number of Mongols died or fled during the chaos caused by the fall of Qing and imposition of Stalinist-influenced policies. This included nearly all the ethnic Han population of Mongolia, who made up over 10% of the population and in the capital Ulaanbaatar made up over 50% the population. There was an element of ethnic cleansing to this since the Mongol leadership believed the Han were going to demographically overwhelm them, even though Han settlement in Mongolia is fairly old since Karakorum back in the heyday of the Mongol Empire always had a large Han community.
