They don't want any war with us but an economic one. They need our business and to keep stealing our tech, and we're inconveniently located for making conventional war. They have millions of young male bodies, many excess to requirements at the moment, to draft into an army of invasion and occupation. They don't have that large a navy or air force. A land war is their best bet.
They're going to keep taking our money, which we will undoubtedly continue stupid enough to keep giving them, and use it to eventually make war on Russia after they bamboozle Putin into expending all his arms and armies in the Ukraine while producing increasing political and civil discontent in his country by "helping" him with a few token armaments and many promises of undying friendship.
Russia has tons of oil plus other resources, not excluding the biggest rights to the probable Arctic resource bonanza of the coming century, lots of space, and lots of agricultural land right next door to them. By the time they get around to invading, it may even have the Ukraine breadbasket of Europe, or at least part of it. Once they capture the Siberian oil, it's on to Moscow.
If the second Mongol Empire lasts long enough, they may tidy up a bit around the edges of Asia where it seems worthwhile to do so and consider annexing some of Europe or Africa. If they have any sense, North and South America are way down on their list of most useful/beneficial/convenient targets available at affordable cost.
The only way I see China launching a major armed conflict with the United States in any near-term future is if we act like total idiots (always a possibility, admitted) or if they somehow completely lose their strategic sense and ability to set priorities. My gut instinct is that their passively siding with Russia and encouraging it to go on fighting in the Ukraine for now is just a shrewd strategic move in a game of Go, meant to mislead and distract attention while they set up their end game.