If China can become a quasi-ally with US to counter the Soviet Union, then it's not outside the realm of possibility that "Reverse Nixon" is also possible: that Russia can be an quasi-ally with US to counter China. I don't see how Russia, a former Superpower, can accept or tolerate to be subordinate junior partner to China, particularly an alien civilization with no shared language, culture, or even ideology like Communism (like old times). You have to have more than just "Anti-Americanism" to form the basis of a long-term alliance, the Sino-Soviet Split demonstrated this.
Thats not entirely inaccurate. Realistically, if western containment of China were to succeed in holding back China to a certain degree in its economic development, Russia would remain in alliance with China, as China would remain the only viable bloc with Russia against American global hegemony. However, if China did in fact reach a GDP of US + EU by the 2050's, it may persuade Russia to join a western bloc, especially if it isn't able to accrue benefits from the rise of china (broadly being increases in per capita GDP and living standards at least matching china by the 2050's.) If china were to reach a GDP of US + EU by 2050's though, other options would potentially exist, such as marshall plans to uplift 1 billion people out of poverty in the Arab World and Africa to bring into a counteralliance against the west.
Either way, global hegemony never lasts and is self correcting.