Heating concept for new buildings - heat pump vs. masonry heater?

I also find the trench collector interesting.

I would take a very close look at the point of economic efficiency. If you hire a company to create the trenches and don’t do anything yourself / can’t do anything yourself (very understandable with 3 children), it will cost you several thousand. And this money has to justify the slight advantage (perhaps COP from 4 to 5)? So, very optimistically calculated, a maximum of 20% of the energy costs. If your annual electricity costs for a heat pump are €900, you save €180 (=20%) per year. If your additional cost for the entire brine heat pump system were only €3600 (one can still dream...), it would only pay off after 20 years(!). But by then something is definitely broken or you have other problems with the water system. Maintenance effort by an external company is also certainly more expensive.
My opinion: Better invest the money in proper photovoltaics and, if economical, storage. That pays off in <10 years with good orientation.

Regarding the masonry heater: Because of the weight (with heat storage stones gladly up to 1500 kg!), you will need reinforced screed. That also costs extra...

Actually, nothing should really break on the brine pipe itself. In return, you save yourself the outdoor unit of the split air-to-water heat pump, which also does not last forever. And the actual brine-to-water heat pump is then comparable to the indoor unit of the air-to-water heat pump.

When it comes to wood, do not forget the risk of physical injury. Saws and log splitters are a bit more dangerous than the button of the heat pump.

Further considerations for the trench collector: planting is only possible to a limited extent (probably only certain shallow-rooted plants). It can cause problems if there is a later desire for a cistern, a pool, or a deep foundation for whatever reason... Overbuilding (desire for a garden house?) is also limited.

Instantaneous water heaters/domestic hot water heat pumps probably consume a lot of electricity or are not far away cost-wise from the heat pump solution?

I would not recommend instantaneous water heaters with 3 children. That is more a case for single or couple households, who otherwise have high standby losses with hot water tanks. You can do domestic hot water heat pumps if you do not have a heat pump for heating, but only use wood. The costs are about 2.5-3.5k material costs + 2 hours installation + the usual surcharge for the boss’s (electric) SUV, so about 5k in new construction. The domestic hot water heat pump is also not more efficient in hot water preparation than the central one.

Masonry stoves should bring a certain thermal inertia but maybe we have to classify it as a luxury

In new construction, everything beyond a heating system is luxury / economically nonsense. Due to the requirements in the Building Energy Act, you already have a low heating demand of perhaps 20-30 kWh/m² per year. Covering that with ONE expensive system is already comparatively a lot of effort, but two expensive systems (masonry stove from 15k€ upwards) will not pay off even without fuel costs.

Thank you for your tips. Now I know what is probably the best economically at the moment. I will have to negotiate about a [Spaßofen] with my government.

Fine dust is also an issue in rural areas. There are nice fellow citizens everywhere who throw everything that burns inside. Filthy pallets, wet wood, gift wrap, and pizza boxes.

We also once had a fun stove in the planning. Somehow the chimney was always in the way and it’s not free either. The stove was gone.