The best-case scenario for sustained Russian rule would be to go native, but that's completely implausible that late. Depending on when exactly it occurs but I'm going to go with the best-case scenario for Russia here. Like, once in in one billion lifetimes tier best-case scenario.
After allying with Napoleon, Russia turns all of its efforts east and experiences wild and unexpected success against China. With France's full support and Britain essentially occupied indefinitely with France, Russia is able to annex all lands down to the Yellow River. However, attempting to establish rule in this region quickly becomes unfeasible and Russian control of the countryside is a fiction within a year. Down south, China is in chaos as Manchu rule has collapsed and competing states vie for dominance in order to push the foreigners out, playing heavily to Han nationalism and ethnocentrism. Russia's heavyhanded attempts at governance ultimately prove ineffective and simply fuel both unrest in their portion of China and the rallying cries of Free China.
After sinking money endlessly into trying and failing to administer China, Russia decides to try for a new approach and divides Han Chinese lands into client states after about ten years of failure. Maintaining control of major coastal cities and foreign relations, Russia's client states are dominated by a Russified clique of Han Chinese and their Russian patrons, largely military men who have manned control of major fortresses which act as a stabilizing factor for the Han Chinese rulers of these client states; nevermind that most of them are privately Orthodox Christians and have personally sworn fealty to the Tsar.
While Russian China settles down somewhat, the feuding between the Free Chinese states creates a refugee situation that ironically, sees many Chinese fleeing north to the more stable and economically productive Russian Chinese provinces which are quickly recovering economically as a result of top-down enforcement of reformed taxation policy. The decade of instability had done much to break the people's faith in previous systems and frankly, the results spoke for themselves. There was, however, an undercurrent of slight Russification in these provinces. Russian businessmen dominated China's nascent industries, the bureaucracy was dominated by Russians and Russian-speaking Chinese, and there was a building boom of Russian Orthodox churches which acted as middlemen for aspiring young men seeking to prosper in the new China, as well as the primary handlers of refugees. It was often recent immigrants that became the most pro-Russia as a result, ironically enough.
As the refugee situation grew more dire and northern China strained, Russia decided to take action and push further south, establishing client states alongside the Chinese coast in a series of wars and crushing the most destructive and anti-Russian factions in Free China, while essentially turning other factions that were viewed as too troublesome to war with into client states. It was a gradual, and long process, but by the end of it, China was largely controlled by a series of Russian-dominated and native patchwork much like the British in India. Peace was fragile, but sustained by the economic revitalization of China in the period following Russian conquest.
- At some point, Russia's attention will be forced West and an opportunistic vassal or two will shake some of Russia's shackles
- If/When Russia suffers a military defeat that ties up most of their manpower, expect peace to shatter like dominos
- However far more prosperous and familiarized with the West and their advances, the wars in China will result in the most prepared and modern army establishing relatively quick rule over the majority of China. Some states may hold out for Russia, others may opportunistically swap sides when the tide turns
- However, this state that now rules most of China is one of the most Russified. It's economy is largely dominated by Russians, it's leaders are Orthodox Christian, and so on. The military is as much Russian as it is Chinese and it's largely tied together by the charisma of its leader. As a result, this state used a pretext of reestablishing order in Russian China in the name of the Tsar as the reason for their military actions. So de jure, the Russian Tsar remains 'Emperor of China' for strictly out of necessity to keep the Russian elements of society placated. In practice, this isn't the case, but Russophilia dominates the upper echelons. An alliance with Russia is quickly proposed to Moscow, the army operates in Russian, as do the upper crust, the capitalists, the bureaucrats, and the well-educated
- Russia, having lost utterly in their war in Europe, are left without much choice but to accept, not willing to reengage in Chinese adventures so long as the markets of China remain entirely open to them. All non-Han lands in Northern China remain under Russian control as do a few key port cities, but the end result is largely a Russian Chinese dynasty.
- The Russian-Chinese border may as well be nonexistant, and Russians and Russified Chinese are the first-class citizens of the state. It's very existence is sustained on the continued economic prosperity of the Chinese people making them unwilling to shatter the status quo. The position of the state's leaders is far more perilous than it'd appear at first glance as without the existence of the Russo-Chinese military class and the incidental means of social mobility that were established via the Orthodox Churches and the military, society would largely collapse and Russian elements in China expunged with swiftness
- The even-handedness of the Tsar is the only reason the state still exists. If Russia decided to declare war for reannexation, the ruling class would tear itself apart into a civil war and the Free China era would return with a vengeance.