Simply being has an effect on carbon emissions.
Even dying and decaying will have an effect.
Like grass
feed ruminates, composting is something that would happen without human intervention.
I worry more about the stuff that we add to the world, primarily by digging up carbon and burning it.
The other thing we do is destroy the forests, grasslands etc, that actively sequester carbon.
Composting can reduce both of these activities.
Compost, applied to perennials, will promote carbon sequesterion.
Making
biochar from the perennials, even more so.
The same biological materials in a landfill will produce nothing positive and contribute nothing going forward.
The process of getting the materials from your house and into the landfill will almost certainly burn carbon would otherwise remain sequestered deep
underground.
Composting takes human burned calories that you would otherwise use or store.
Every useful thing you grow from the compost is another thing that doesn't need to be transported to your location using fossil fuel.
It's also not fertilized with petrochemicals, which would likely have been extracted , transported and processed by more fossil fuel.
Further, no carbon sequestering bioms are being destroyed to grow it.
Composting in a biodigester could capture greenhouse gases, and even displace the use of fossil fuels, but it's hard to implement on a small scale.
I think excess biological materials
should be used as construction materials,fed to livestock, burned cleanly to displace the use of fossil fuel, or composted, in roughly that order.