India wanted to take its own advantage by playing neutral between US and China till Galwan happened. Prior to Galwan, India's strategic soft play with west was largely to balance China's strategic friendship with Pakistan. Frankly I don't know what benefit did Galwan give to anyone. If there are right incentives in being friends with China, I am sure India will utilise them but currently I do not see them and in short term things will have their ups and downs. Longer term India and China will have to reconcile with the other's strategic strengths.
Right there you are spot on.
This Ladakh crisis, what you referred to as "Galwan" in general, does not benefit China. It does not benefit China to flare up a border dispute it has been trying to offer demarcation and compromises to with India who refuses to settle it due to India wanting Aksai Chin and unwilling to compromise on any deal without Aksai Chin. It does not benefit China to go to war with India regardless of how positive a result may be for China. At best it sacrifices material, time, money, and lives to gain a slither of land - the remaining 20%. At worst it loses Aksai Chin. So why would China have done this. The answer is obvious, China didn't flare this thing up.
Believe me, Indian leaders do not want friendship or cooperation etc with China. They have reasons not to for sure, but please don't assume they have carried themselves in good faith wrt relations and tensions with China.
Galwan since it happened, can only be resolved by China in one way. Either China somehow gets India to demarcate, understand and accept that India will not get Aksai Chin and the details of where the border will be set probably will be between the blue line where China controls since 1962 and the end of China's official claims. Of course China will compromise as it had offered in the past, as long as China gets Aksai Chin. Failing this, since India will find it unacceptable, China will try to make this slither of land a buffer so that India has no access to patrolling or controlling any part of Aksai Chin. This is a work in progress and Indian troops surely still have not vacated certain parts of this narrow stretch.
A war does not benefit China. It does not want such a distraction from bigger goals. A tension with India also does not as China would not wish to divert forces and risk any multifront war. It was India with everything to gain by making increased patrols and moves on that slither of remaining disputed land in Ladakh (not incl Aksai Chin since that's been firmly controlled by China since the border war).
India considered its chances for salami slicing via patrolling and temporary structures within this stretch of land to be at worst responded to by China with diplomatic complaints and nothing more as China was distracted with covid outbreak in early 2020. It also considered that China would not escalate the conflict because salami slicing has been practiced by both with pretty good mutual understanding of how it works. India was half right on the latter. It simply did not expect a fairly strong reaction from China. Anyway the rest is history now.
Would both move forwards in good faith depends on how we finish this resolution. How is the buffer deal going to go for the rest of the area under standoff. How will demarcation attempts go. How will India and China play the extended geopolitical game now with the rest of the region etc. I do not have hopes that the two can form a better understanding and de-escalate the bigger underlying tensions that have come around since Doklam crisis and peaked with this one. Especially IF India and Pakistan tensions increase, China will almost certainly be backing Pakistan which would contribute to further unease between India and China.