Cost per construction cubic meter: rule of thumb?

Precisely because the ceiling height is included in the volume, it should be more accurate, the extra wall

That is not true, because the costs still scale more strongly with the area than with the volume. If, on the other hand, I have the ceiling height as a known variable, it obviously doesn’t matter which measurement I use, then I can convert one into the other. But: If I don’t know the ceiling height, and that is assumed now, then I don’t know if a new building with 1,000 m³ is a bungalow with 400 m² floor area and a low ceiling, or a "normal" one-and-a-half-story house with 200 m² living space and an unheated attic.

When it goes to the extremes, any simplified standard calculation becomes increasingly inaccurate.
In our calculation, after area (1600.-) + 50k for the basement, it would be 258,000.-, and after volume with the 300.-€ assumed by the bank, approximately 250,000.-
With the corresponding values, you will come to a similar result.
The prices will anyway depend very individually on special features.
If I have floor coverings for 100.- / m² compared to 30.-, that already makes 10,000.- for a house with 130m² of living space.
It is also no problem to plan 10-15k€ more for the bathroom, plus electrical work and a bit of knick-knack here and there, and then the different calculation plays a rather minor role.

Now you have named three trades that only scale with the area... I'm opting out

??? In the bathroom, it rather depends on the equipment. I would rather imagine one expensive bathtub instead of 3 cheap ones in the bathroom, even if I have more space. Likewise, I only have one shower and one (double) washbasin. Whether you choose KNX for electrical installations also has absolutely "0" to do with the area, as well as equipment like built-in spotlights, (wireless) dimmers, LED or halogen, number of network sockets, TV sockets, etc. And especially if, for example, the floor coverings depend only on the area, then the error in m² calculation between the different floor coverings becomes all the greater the greater the difference in living space is.

Argh... The QUALITY of the equipment is reflected in the price per unit (area or volume), not the QUANTITY.

When do you have more sockets, more flooring, more showers? With a lot of floor space, or with a lot of enclosed space? Do you still have sockets at 2.50m height with a room height of 3m? Do you perhaps stack 2 showers on top of each other with a room height of 4m? Certainly not, but with a lot of floor space you might have one more bathroom, or 2 washbasins per bathroom instead of one.

But it is clear that the room is (roughly speaking) length x width (=area) x height, right? In this respect, the area is also taken into account in the enclosed space. In the end, similar values come out with the corresponding factors, which is why there are both estimates, and that’s all there is to it.