The methane will eventually break down and be part of new plants, but in the meantime it will heat the planet much more than if it hadn't been there. Think of it this way: industrial scale cattle farming essentially makes and feeds biochemical reactors that turn hydrocarbons into a gaseous form that maximizes their global heating effect. Consider the counterfactual where we don't stuff billions of fart machines full of corn.
> The methane will eventually break down and be part of new plants
To be exact, excess methane go in the high troposphere, where it is broken down in CO2+H2O (the half life is very short, I don't remember which is which but it's either 5 or 20 years). So in any case, it accelerate climate change.