You say its Putin's war I thought? Do you know what a proxy war is?
A proxy war is where you get someone else to fight your war for you - you provide all the weapons and pay the monetary cost.
So yes NATO vs Russia using Ukraine to provide the troops and NATO provides weapons and money.
China vs NATO would imply that China is using Russia to attack NATO and is providing lethal aid and all funding (like the USA is)
You claim Russia is not providing the weapons or funding but you also say NATO led by USA is not a party to the war? You have to make up your mind on the USA role.
Are you saying it is a Chinese/Korean proxy war vs Ukraine?