pre 1900 - Chinese influence is going to be limited to the Chinese sphere areas. however tales from the east will move west.
your biggest problem is that the seat of power is in the west and looks to the west not the east ( or south and east in this case )
There is a lot of nothing in between even the greatest extent of Chinese borders and Moscow.
So your best bet would be to have the Khanate continue to some degree or for longer and remain more mongol than turkic. After the Slavs threw off the Golden Yoke and Christianized eastern influence was pretty much over after Peter Alexeyevich came to power pushing the byzantine practices and eastern connections on the back burner in order to modernize and compete with the threats from neighbors that were much closer such as Sweden and Poland.
Chinese influence was greatest in southern central to eastern Russian regions. By the time you get to Perm and the Kama river you are just to far away pre modern travel to have a great influence. Western Russia is highly Slavic and urlic to the north blending into Baltic and western Slavic cultures the further west you go. Central Russia is highly turkic.
to the south you turn from Russian Slavic to Ukrainian Slavic culture to turkic mixed with Balkan cultures.
To the east you go from Russian to turkic, Persian, Armenian and Mongolian.
For Chinese influence to spread they would need to go through Persian and turkic groups first.
China and Russia were both vast nations. Russia more heavily focused in the west with its capital at St Petersburg and China to the far east in Beijing.
Okay, but what if Russia gets influenced by China by having China setting up base in Russia after it has had a crippling defeat. I'll put this admittedly simplistic idea as follows.
Due to some POD divergences, Germany forms with Austria as apart of it in 1848. Germany then goes on to keep an alliance with Russia that it subsequently forms. Later, Germany gets into a war France, Great Britain, and Italy that sees it become the dominant power in Western Europe. The other three nations are no longer great powers. Germany was able to win this war thanks to the food and oil that it gained from Russia. Germany expands it's already existing colonial empire in Africa and Asia and gains lots of resources there. It ends up with the world's largest navy that helps to guard and deliver many resources to the metro-pole. But, German leaders come to see Russia as a final threat to Germany. This is because they fear how powerful Russia would be if allowed to fully industrialize. So, they end up funding ethnic rebellions throughout the Russian Empire that eventually leads to Russia accusing Germany of doing this, which they are, and going to war over it. Germany loses access to Russian resources, but is able to sustain itself through overseas trade from the Americas and from it's own vast colonial empire. They have also been funding China's industrialization, so as to open a two front war with Russia that will force it to have to divert it's troops. Americans have also been giving lots of investment into China because they see the chance to make a lot of money from it.
This second World War ends in total Russian defeat, with Germany and China forcing the nation to balkanize, even in Western Russia, which becomes a brutal nightmare as German nobility are giving their own private fiefdoms to rule over. China gains control over Siberia and Central Asia, which are left as puppet states. That will be explored later.
They also gain territories that used to be Chinese in OTL. Basically the bottom plus some other territories, such as Outer Manchuria and a few others.
German control in Western Russia is very brutal. There's no Genocide, but German troops are willing to kill lots of Russians to make a point against rebellion. Famines, death squads, and firebombing of cities, are commonly used to make an example out to other Russians throughout the fiefdoms. Ukrainians, Belorussians, Finns, Baltics, Caucasians, and other ethnicities don't get these since their regimes are willing to work with the Germans under the idea that the Germans came to liberate them from the Russian yolk.
Meanwhile, China, due to their parts of Russia being less populated, just set up vassal states and as it is a Republican nation, there aren't necessary any nobility to give plots of land over to. At most, it they just become places for large Chinese corporations to have pull in. This means that Siberians and Central Asians get lots of Chinese products. China later decides to built an alt version of the Belt and Road project, and so Siberian city-states, though those have lots of land, and Central Asia get heavy investment into their infrastructure and Chinese works arrive to set up businesses in those areas. The Chinese language becomes a popular thing to learn in those areas, with local governments being encouraged to teach it. It's relatively easy, as lots of Chinese cultural programs are distributed in those regions. China has also set up lots of military bases in those regions similar to how the US did in Europe. Due to the cultural barriers being gradually broken down, there are more and more intercultural marriages between the locals and the Chinese. There is some resentment for this for from the locals, but not much can be done by them as ultimately, China is in charge, and most people are okay with it(not really happy, but mostly apathetic, as it's not like they can strike out on their own, and it's not like China is that bad a ruler).
Meanwhile, back in Western Russia, Germany has begun to regret it's part in helping China to industrialize as now Chinese guns are being distributed throughout it's colonial empire. There's already a sort of Cold War that has begun between the superpowers of China and Germany, and China is doing a lot on it's part of the Cold War by aiding rebellions in territories controlled by Germany. It's not hard to start up rebellions, as Germany is a pretty vicious colonial master as it uses the native populations to produce lots of luxuries for the German people, and it does this by forcing them to work in horrendous sweatshops.
Throughout this Cold War, Germany has been spending a lot of it's money on trying to preserve this power for itself, but it's quite difficult as it has what are basically a dozen Vietnam Wars across Africa and Asia. Over time, spreading from East to West, Germany loses each of it's colonies, including what it has in Western Russia. In that area, there are a bunch of calls for unification, and they are becoming harder to put down thanks to Chinese funding of terrorists. Eventually, the German Army is forced to leave. But before they do, they leave Western Russia with a lot of destruction, both industrial and agricultural, and a famine ensues. With it's bases east of the Ural and in Central Asia, China is able to come and aid in the rebuilding of Western Russia.
Western Russia is able to reunify, but only in the mostly Russian areas, as everywhere else that is non-Russian majority are still willing allies for Germany, and there aren't really any desires to trade a German master for a Chinese one, seeing as how they were treated much better under the Germans, than they were under the Russsians. Meanwhile, unification with Siberia is a complicated issue, as although many Siberians speak Russian, they have been heavily sinicized over the decades. And unification in Western Russia is already a big issue, as much of the infrastructure is directed toward bringing resources towards Germany rather than sharing it among each other. For now, China essentially gives West Russia a Marshall Plan-esque treatment, as the story that occurred in Siberia and Central Asia, now occurs in Western Russia, but it's less bittersweet( if you can call the other one that) as a common image is a Chinese nurse sharing Chinese snacks with West Russian children who had spent much of their lives working in a factories. Think the Americans in Europe and Japan after World War 2 for this image. After many, many years, West Russia is rebuilt, though a great loss of Russian cultural heritage has been lost, but in it's place is a hybird of Chinese and Russian culture. Russia is now wholly within the Chinese sphere of influence and considers itself more Asian than European. It's not uncommon to see Russians with Chinese ethnic features, though a lot of people still look like how most Russian did nearly a century ago. The relation between Russia and China is now similar to the one that OTL America has with Japan and South Korea, if even closer than that due to lots of migration from China to Russia, along with even more cultural influence.
Okay, so this is my very simplistic vision for having China gain lots of influence in Russia. What do you, and others think?