That 4kg CO₂e of emissions per kg composted anaerobically is roughly what you get in landfill, too. However, conditions vary a lot at landfills, from 1 to 12kg CO₂e, and the emissions due to the transport are smaller than that; a truck carrying 10 tonnes of rubbish burns about 1lt of petrol every 5km, generating 2.32kg CO₂e, and on average travels 50km daily, and thus the 10,000kg of rubbish require 23.3kg of emissions to transport, or 0.00233 kg CO₂e per kg.

Let's be pessimistic and assume that the processing at the landfill or large compost adds nine times as much again, giving us 0.0233kg CO₂e. This is rather small compared to "1 to 12". Single contributors which fall far within the margin of error of the major contributor can be safely ignored.

But even if it were 10kg CO₂e, or 1,000kg CO₂e, avoiding extra emissions does not make your compost carbon negative, which was my point.

In areas where there's a "green waste" collection programme, they'll have emissions due to transporting it, but will compost it more efficiently, making sure it's always aerobic and not anaerobic, so that on balance the council can compost with less emissions than can you.

But most areas don't have green waste programmes, and in any case you'll want compost to contribute to your own plants which are carbon-negative. So composting at home is usually a reduction of your personal emissions, no doubt about that. But it's not zero carbon, nor negative carbon. And your original statement that "those [carbon] calculators don't take into account the composting, which reduces our green and brown waste to zilch" strongly implied that your green and brown waste were carbon neutral, or even carbon negative. They're not.