Indian thinking can probably explained by this article:
This articles how many Indians believe they can surprise China with a strong strike that will cause PLA to have huge losses which will ultimately allow India to negotiate a solution in its favor. Even if China won tactically, if they take huge losses then it will be India which will be able to gain strategic victory.
My thought is: the current political climate in India is extremely nationalistic and jingoistic. Anyone following Indian media can see a trajectory where only military strength and toughness is glorified. It doesn't matter what losses India takes as long as they appear tough. There is a strong thinking that India have been soft in the past with Pakistan and China and muslims. Now India will not be soft and will go for bold moves under the new Modi govt. This is sort of the selling point of Modi and BJP that they will be tough while Congress have been soft.
I think there is a strong appetite for war in India right now. There is a strong appetite to prove its toughness and boldness. Indians don't care about losing right now as long as they appear tough and glorious. Case in point, the Balakot strike which was a net loss for India in every measure and humiliated India and really boosted Pakistan's prestige. But Indians did not care. They were happy that India did something to Pakistan regardless or the outcome. India is an angry and hungry nation right now. They think China will not go for all out war. And even if it does, India will somehow inflict huge losses on China to force them to back down.
I don't see a similar appetite in China. So, India will keep provoking China. They will always be bolder than China in the border fight. Verbal warnings will simply not work. Chinese exercises will not work since India thinks China does not have any interest in fighting a war with a "tough" and "bold" India.
So, what does China think about this matter? What does Xi Jinping think?
I really don't know. Xi Jinping has been extremely pragmatic and willing to swallow a lot of humiliations if it meant China could maximize its benefits and minimize its losses. Xi Jinping has also been systematic and bold in pursuing Chinese interests as well.
Considering that the new cold war is rising fast, he could decide that fighting a full-scale war will be a net loss for China. So, he could swallow a humiliation and negotiate a solution that is slightly more advantageous for India, thus, giving Modi the public win.
Alternatively, maybe he has had enough of Indian provocations regarding Kashmir and joining the Quad and many other provocatives moves by Modi and has taken a fundamental decision to teach India a lesson. The fact that India is sinking under Covid and economic slowdown is the perfect time to strike India heavily.
Whatever the decision was, it has already been made.
Maybe, there is a third way. Which is just simmering tensions and skirmish for many years. This is what happened between 1962-1980s between India and China. I think there is a strong chance we will see border firing and artillery firing similar to how it is in India-Pakistan border. This type of firing and tension could continue for many years.