It emits no more CO2 than the thing being composted soaked up when growing. So it will emit less than the amount the mushrooms absorbed. This is the cycle of life. This is not a problem.

The problem is when you emit CEO that has been absorbed over hundreds of millions of years and fossilized in oil and gas all within 100 years or so.

CO2 that was sequestered from the atmosphere. That's very different than CO2 in polystyrene which is fossil fuel derived.

If you're doing it right and using it as soil ammendment, a portion remains in the soil, building up the soil humus. In the long run it can be carbon negative.

I could see making something like this from food waste and then just burying it in the ground.