I don't see going all "fuck you I'll fight all of you at once" as a good idea. We have a legit mandate right now to crush US because they've pissed off so many others, but if we crush Russia afterwards, it shows that China is only about might makes right. And sooner or later, it might take 50 years or 100 years or even more, but the possibility of a hostile world overcoming China's blockade exists, or some can argue will inevitably happen.
The US has indeed upset, if not destroyed a many nations and peoples. However, that is simply the nature of hegemony.
If you're a shot caller, you're going to make decisions and set conditions that will please some and upset others. There's no making everyone happy.
With that said, should the world return to Pax Sinica, the Chinese should be prepared to be hated, feared and respected by the rest of the world just as Uncle Sam has.
I am not unique in this thinking, many people in China think this way. In fact many schools have text books that say that Outer Manchuria is Russian occupied land which one day will be retaken to complete the rejuvenation of the Chinese Nation.
There isn't a practical need for the Chinese to force Russia's hand on historical territorial issues. All the Chinese really need to do is to be patient, as they have been elsewhere, and let Russia run its course.
Once Putin leaves office, odds are Russia will experience a great deal of turmoil as Putin's lieutenants compete to fill the vacuum.
Should that get especially ugly, Russia will further weaken and fragment itself, and Russians living in its Far East will not fear the possibility of Chinese rule, but ask for it. Though it will obviously start in de facto rather than de jure terms.