I'll provide some quick thoughts in case no one else answers in a better way.
I don't know anything about farming in Pakistan in particular, but I'd be surprised if there weren't the same welfare issues as elsewhere. E.g., egg-laying hens are probably raised in cages which is very bad for them. So by being vegan, you would save tens or hundreds of animals per year from suffering in expectation. It's particularly important for animal welfare to avoid eating chicken, eggs, some types of fish, and other small animals.
However, you could potentially help millions of animals by becoming an animal advocate. I don't know about Pakistan in particular, but in most Asian countries animal advocacy movements are very small or non-existent and people who would start such movements and think about cost-effectiveness would be extremely valuable. I see there's an article about it here.
Also, Our World in Data's assessment you cite is about fossil emissions. It mostly depends on industries. It doesn't include cow burps which are a big contributor to climate change. I don't see much reason to think that choosing a vegan option for a meal in Pakistan would have less impact on climate change than doing it in a Western country. But this is not my area so I don't know.
Hey DoGooder!
Welcome to the forum! This is indeed a super important, as well complicated question. I don't have a confident opinion, but thought I would point out some potential cruxes that might help you to form a view on this!
There is probably a bunch of other considerations that don't come to mind at the moment, but hope some of these will be useful!
Also I just wanted to mention that I know a couple of EAs who are originally from Pakisan but live in Hungary, as well as a person living in Pakistan - if you would like to be connected to them ping me a private message!
Thank you, grego, for the resources. I'll make sure to go through the links and carefully consider the information.