The strategic interests of China, India, and Russia all lie in different spheres. This is why there is little or no interest of a conflict between those three countries. Sure there is currently a border dispute between China and India, but it's nothing that can't be resolved with enough time and good faith negotiations, just like how China and Russia resolved all of their border disputes.
The only reason why China and the US is on a conflict course is literally because the US needs to maintain a global hegemony and China's rise is challenging that hegemony. China, in the foreseeable future, has no interest in a global hegemony, and I would argue that it should never seek one. If you don't seek hegemony, then you don't need to suppress anyone.