Poop decomposes and becomes greenhouse gas. Fancy new filtration plants capture some of that gas and produce electricity with it. Most is not captured.

Fertilizer mainly helps 1year crops grow, aka food. Not forests that will bind carbon for hundreds or thousands of years. The typical large scale agricultural industrial operations cause more release of carbon than they bind it.

A very large part of the produced fertilizer is used to, often on land where there used to be carbon binding forests, grow soy, corn etc to feed enormous amounts of livestock. Which we then eat. It is a manyfold less efficient way for humans to consume animal protein rather than plant proteins. Producing and using lots of artificial fertilizer is for sure not a positive effect on global climate change.