Indian leadership hasn't been going on TV prior to the Pahalgam attack and putting out bellicose statements like Hindus and Muslims can't live together - Pakistan did. Also India isn't stupid to invade a nuclear armed country with a first-use policy.
The above incursions are the usual dance we see with India and Pakistan (and China), that we see every few years. Except this time, Pakistan triggered it by attacking civilians, just like 26/11, while even Indian support of Pakistani terrorists such as the Balochistan Liberation Army has never led to a large-scale slaughter of civilians in Pakistan.
Pakistan messed up big time, they'll chalk up the L, it will be a few tense words for some time, and then things will get back to where they were before.
Underlaying this line of reasoning is an assumption that Pakistan makes coordinated, coherent, and more or less rational decisions. But Pakistan is run by the military with civilian leadership being a farcical fig leaf. They routinely fall into prolonged periods of martial law, and arresting former prime ministers is the norm. What's more, Pakistan's military is divided into numerous factions which are operationally independent and have their own internal politics going on.
Therefore, any analysis of the form "[hypothesis] is unlikely because it would be irrational and uncoordinated" is extremely dubious.
On a side note, the Gulf states being involved in negotiations pretty much means the end of the US as a diplomatic hegemon for the region.
The Western consensus about the outcome of the invasion that of a rout.
> both sides are showing aggression towards each other and weighing the costs of going to an all out war
Outside an Indo-Chinese land war, the only paths for industrial war emerge from New Delhi. Either in reacting to a miscalculation by Islamabad. Or because India's going imperial. The latter would be shockingly like Russia invading China in both scale and capacity to get drawn out by outside backers.