The only relevant data I could find in those links was from "ecologically sustainable recovery of bio-waste". A figure on page 38 suggests that bio-waste recovery could save between 29 and 194kg CO2e per ton of waste, but the breakdown does not appear to include the emissions involved in the collection of domestic food waste and the accompanying text acknowledges that the data is not based on a full lifecycle analysis. I cannot find the source document cited in the figure, possibly because of a translation issue from the original German.