Impact of India-Pakistan nuclear war on x-risk?

Last month I was involved in a conversation thread about what the impact of a hypothetical nuclear war would be on existential risk.

There are many potential nuclear war scenarios which would have varying impacts on existential risk. It’s difficult to know where to start to gain an understanding of the long-term of nuclear proliferation.

For concreteness, consider the case of an India-Pakistan nuclear war.

According to Local Nuclear War, Global Suffering by Robock and Toon,

India and Pakistan, long at odds, have more than 50 nuclear warheads apiece; if each country dropped that many bombs on cities and industrial areas, the smoke from fires would stunt agriculture worldwide for 10 years.

[...]

1 billion people worldwide with marginal food supplies today could die of starvation because of ensuing agricultural collapse

Note that this would presumably cause some degree of chaos in the developed world.

I have not yet investigated the credibility of the papers’ claims. However,

Suppose that an all-out nuclear war between India and Pakistan were to occur and were to result in climate change killing 1 billion people. Then would the probability of a positive singularity increase or decrease and if so why?

This question seems very difficult to answer; maybe altogether too difficult for humans to answer. I welcome responses raising relevant considerations even in absence of a good way to compare the relevant considerations. Please read the linked conversation thread before commentating.