In the KfW leaflet, I actually did not find a minimum size, only "Residential units are rooms in residential buildings that are located in a closed context and intended for permanent residential purposes, which allow for running a household (own lockable access, room, supply connections for kitchen/kitchenette and bathroom/WC)."
Currently, only program 297 would be possible; we are out for the 300 because the property already exists (sounds strange but that's just how it is). Since we would build without QNG, it would be "only" €100,000 per residential unit, for 10 years at about 3% less interest per year than is currently typical in the market. We would like to take advantage of this, especially since with double funding we could repay one of the loans by 10% to close it at 0.01%. In short, we would gladly take it.
A technical room of 8.1m² could probably be a bit larger — washing machine, dryer, sink, a somewhat larger electrical cabinet because of the granny flat and photovoltaics, inverter, at least space for a storage battery, ventilation system, space for a vacuum cleaner. Although that could also go into the pantry, but I could definitely fill a cabinet for "bulkier" stuff there. And actually also a drying rack, so you don’t have to throw everything in the dryer or for everything that is not allowed.
The tree expert would prefer if the new house in the front southern area does not extend beyond the old cellar, so that the cellar wall could be left standing and nothing would change for the roots — that would be easiest and best for the tree. The alternative would be a root search trench dug by hand, basically an archaeological excavation with a brush to expose all roots, if possible to redirect or cut cleanly with wound care. That would definitely involve additional costs ;) But as I said, I will ask him (with 10m width and 13.5m depth, he was very nervous; the current design would of course be more relaxed). We have planned a little beech budget, but certainly not enough for weeks of brushing.