Yes, the Indian government behaved foolishly, but the Chinese government must try to balance its interests and not push India to the arms of the West. The goal should not be to publicly humiliate them or to take out their force so Pakistan will get back Kashmir. That would push them into the West camp. The goal is to ensure that the Indian military and politicians know privately that their acts will be futile and retreat and de-escalate on their own. India can either take the humiliation of retreating now or be dragged into the quaqmire of a never ending resource drain. It seams the politicians are now choosing the latter now. At some point, the political situation may change and allow them to back down.That’s because it was always about internal politics to start with.
The Indian government never wanted a fight with China, because they know full well they would loose, and loose horrifically.
They just drank the western Kool Aid and thought China was absolutely destroyed by Covid, so thought they could kick China while it’s down and take advantage so they can brag to their domestic audience about how mega power India is that it can take Chinese lands and China is too afraid to do anything about it.
They knew they fucked up as soon as they saw the scale and speed of the PLA mobilisation and was trying to back down without loosing too much face when that idiot officer who watched too much Bollywood BS thought he would take matters into his own hands and lad a kamikaze charge against the PLA, who beat the Indians so badly they literally killed themselves from fleeing so hard.
That forced India to double down and remain engaged rather than withdraw like they planned (hence the emergency winter clothing whip around with western powers, and future tech chimney stoves), but in reality it was all for show.
China OTOH decided to make it a teachable moment and physically moved in to occupy all of its claimed territory and the mighty Indian military did nothing other than complain. The lesson is that we can be civilised and try to negotiate a settlement, but if you are going to behave like a spoilt child, you will be treated as such and have your toys taken away.
Strategically speaking, I think if India is moronic enough to push China into a war, China will pursue a punitive war strategy and effectively bleed the IAF down to the bone while obliterating key Indian defence related factories and munitions dumps.
The goal is to probably teach a lesson beyond what was done in 1962 and effectively make the IAF extinct while obliterating as much of the IA’s cream forces and equipment as possible such that Pakistan can pretty much just walk in afterwards and take all of Kashmir by themselves.
China will want to avoid being engaged at the same time as Pakistan to maximise Indian humiliation by not giving them even the fig leaf of being ganged up on to hide behind; and also to allow China and Pakistan to pursue their own respective strategic objectives without needed to consider the needs and wants of the other (China will be keen to not take any territory behind what it has always claimed to make it clear it’s war is not one of territorial expansionism, while Pakistan would be keen to liberate Kashmir, fighting together means one or both sides needs to sacrifice their own core objectives, while fighting concurrently means both can achieve all their key objectives without needing to compromise).