Cows produce methane which is a more potent and dangerous GHG. Last I remember cattle produced 6% of the world's GHGs in the form of methane. Your own graphic shows this with "Livestock and Manure" at 5.8%. This is why environmentalist are buying up farm land and turning it back into wild land, to stop the cattle industry. Where I live there are 'public land trusts' that buy farm land and turn it into wild land. I think this is the ultimate objective of Bill Gates buying farm land.

Certainly agriculture is not the only cause of methane. Landfills and most critically leaking pipelines are. In California they fly planes over the state to survey methane production. The research is here: https://ww2.arb.ca.gov/our-work/programs/california-satellite-partnership/california-methane-surveys The main emitters are landfills, and the oil and gas industry, but dairy farms are a significant source also.

On a personal note, I was a vegetarian for 20 years and this was one of the reasons. Unfortunately I got very sick about 5 years ago from being a vegetarian. It is possible to eat healthy (with a lot of money), but more often than not, one ends up eating a lot of processed foods. For me the big thing is vegetable oil. It is worse than sugar or corn syrup. It is amazing that vegetable oil is in almost all processed foods. This is what makes being a vegan so unhealthy. All those fake dairy products are either soy, vegetable oil, or some other unhealthy processed chemical.