Regarding construction costs, that also includes heating.
I would install neither a heat pump nor a gas boiler in a new build.
Wood gasifier with large buffer and solar thermal, and that's that.
Of course, you have to be into that.
Personally, I would want to become as independent as possible for the next few years.
And for a new build, that's enough if the wood gasifier runs twice a week in winter.
You do need a bit of space, of course.
Air-water heat pump + photovoltaic is definitely a good solution.
There doesn't seem to be a royal road, unless you set up multiple solutions in parallel - just in case.
Photovoltaics would have to be very large to run the heat pump in winter. Apart from that, the photovoltaic system or the inverter shuts off anyway when the power grid is down. Unless you have an inverter with island mode, which usually cannot supply the whole house but, for example, only provides a Schuko socket (which doesn't really help the heat pump either).
Wood gasifier... yeah, you have to want that. Here in the new development area, there's a multi-family house with pellet heating; that thing is constantly broken, it stinks, and every four weeks the truck comes to "refuel" and wakes everyone up. Surely mistakes were made there that can't be attributed solely to the technology itself, but still... in my opinion, outdated.