Methane can be and sometimes is produced from biomass.

And there are a few plants in operation that produce without any fossil inputs, but most of them aren't switched over yet, mostly because green hydrogen production isn't at the necessary scale yet and will probably be used for steel making first.

Perhaps a simple explanation would be to quantify the inputs and outputs, maybe from year to year. For instance the carbon footprint of farming should be shrinking if all of these green measures are coming online.