It's only somewhat of a problem for China if Russia can't hold the land bridge and the separatist territories. Which is far from indicated right now.
For China it doesn't matter too much if Russia annexes almost all Ukraine or just the separatists. They need the war to keep NATO aggression down, keep Russia loyal and buy time both for economical and defensive developments.
Perhaps a completely disarmed Ukraine will make it easier for China to counter threaten in Europe together with Russia later, but that is a pretty far out scenario.
I think right now the biggest battlefield of the cold war is in automobile and semiconductor industry. China is advancing towards majority and eventually monopoly in these 2 very major sectors, and America is not even able to contest the former. The same tale as happened with drones, solar panels, home appliances etc will happen here again.
The last cold war only had proxy wars in it, and while its true that we see extremely bellicose language, threats of territorial aggression, both from state media and state representatives on US side, it is questionable if US dares to start a direct conflict, especially after seeing Russia struggle in Ukraine fighting a 1/3rd population 1/8th gdp enemy.
Russians can cope with struggling because they're not on a timer and their population is more or less loyal. Will the same be true for America?