Earlier quoted context omitted.
Methane is produced by anaerobic decomposition; composting is defined by the regular aeration (and sometimes watering) of the compost pile, which allows aerobic bacteria to break down the pile more cleanly. You do still get some GHGs, but much less. See: https://www.agric.wa.gov.au/climate-change/composting-avoid-... https://ww3.arb.ca.gov/cc/compost/compost.htm
Your own references point out that aerobic and anaerobic composting are different processes; the latter, which is most of backyard composting (if your heap ain't hot, it ain't aerobic), produces about as much methane as a landfill does, without the ability to collect and burn off the methane. It boggles me that people emotionally or tribally react to a fact about how chemistry works, google things which support their…
A little methane from the back yard is still better than landfill. But the math for commercial composting vs amateur might need some scrutiny. Transport to the composting facility should also be part of the arithmetic there.