I'm not convinced that China has much of a stake in the outcome. Maybe the war itself serves their purposes because they want Russia to be weaker and have fewer trading partners to choose from, but whether Russia wins or loses in Ukraine, Russia will (short of a major internal political collapse) continue to sell gas to China. The risk that Ukraine or anyone would invade Russia and force a regime change is low.
Same with Iran and North Korea. They might supply weapons because Russia is paying them for it, but they don't have much to gain if Russia were to win.
It's possible that Putin's decision to invade was made under duress, but if so I think it's more likely that it was some faction inside Russia that was twisting his arm rather than an outside faction. (Xi /may/ have set up Russia for failure by requesting that the invasion not happen until the Olympics were finished and the rainy season had begun, but I think that's just idle speculation. I don't know if there's any real evidence of that.)
China and Russia want a world where big countries bully small countries, and the small countries dont find safety in numbers. If russia gets away with ukraine, so can china with taiwan. Thats their stake.
No, its a China/North Korea/Iran vs. Ukraine proxy war.