Not really agreeing with the idea regarding Korea.
Firstly, North Korea is a very useful card for China to play with, which is why Pyongyang and the Kim Dynasty are kept alive until today, and also the reason China would never allow North Korea to collapse. There are also lots of ways China could use North Korea for her own advantage whether there be a war or not, so why should China throw away that card so early and so easily?
Secondly, fighting a war is a very exhausting affair for just about any country in the world. Just look at how Russia is still struggling with Ukraine that has the backing of the entire NATO - And that is still without direct NATO intervention. I'm not sure how Russia would've hold up to an all-out NATO assault without relying on nuclear weapons to hold them off.
Could anyone have imagined how challenging and difficult it is for China to fight in a major war over Taiwan, especially with the near-absolute guarantee that AR over Taiwan would invite military intervention the US and their allies? Unless Xi Jinping wakes up today and sees that the PLA has twice the size and firepower of their American counterpart, I don't think anyone in the PLA CMC would be eager to open another front that would split their attention and focus away from Taiwan.
Thirdly, if anyone has observed carefully, South Korea is comparably more benign regarding the Taiwan issue than their Japanese neighbour and their American overlord. You don't often see Seoul making openly confrontational statements and moves against Beijing on Taiwan as much as Tokyo and Washington DC. Therefore, if South Korea can be pressured into not getting directly involved in a hot conflict with China over Taiwan and/or North Korea, why should China not take the opportunity?
Moreover, there is the problem with the Himalayan frontier - Notice how the Indian foreign policies have been getting more aligned with the West over the last couple of years? The IAF just sent a couple of their fighters for a joint exercise with the JASDF a couple days ago. This is coupled with so many Jai Hinds out there from bottom-to-top in India calling for war with China, and the recent suggestions by the Indian Foreign Minister that they may no longer abide by the One China Principle regarding Taiwan.
Therefore, does anyone believe that in case China is busy with AR over Taiwan, India would definitely keep their hands to themselves and absolutely not trying to open another front with China in the Himalayas - especially if it's the United States that is secretly backing New Delhi to do so in order to divide China's war effort from Taiwan?
Hell, we have all seen that as Russia is stranded in Ukraine, flames were set all across Russia's backyard (we call this 俄罗斯后院起火) - We have Azerbajian picking a fight with Armenia once again; We have Russia getting not so frenzy with her Central Asian neighbours (Kazakhstan in particular); and then there's Turkey who once again invaded Russia's ally, Syria.
So, if China opened a second front in Korea while still fighting in the first front over Taiwan, then suddenly India decided to open a third front in the Himalayas - Could China reasonably and effectively handle all three fronts simultaneously and achieve victory over all three frontiers without suffering catastrophic casualties on her own and/or causing nuclear war? I afraid not.
This is especially without Russian support and intervention on the Chinese side, as Russia would have been obsessed with security issues in Europe after the ongoing war is over anyways. The only thing I could see Russia be useful for is by dropping nukes on India, but that is something that's very unlikely going to happen.
All-in-all, China is very much alone, when you start to think about it...
Plus, I'm concerned that some of the guys here are getting overconfident with regards to China's warfighting capability against her peer opponents.
