Cost estimation of house to determine the budget for the land

Nonsense. You are even allowed to install an oil heating system if you really want to.

Why does it have to be geothermal energy? This may further limit the selection of the property, as, for example, geothermal heat pumps are often not allowed in [Wasserschutzgebieten].

Quality of the building materials/products

Facing preferably with real clinker bricks.

Geothermal heat pump

Triple glazing

Wood floor look

Engobed roof tiles,

Slate roof

Everything more expensive than standard. Then there comes the fancy bathtub, the rain shower, a few nice-to-haves in the electrical installation, a bay window, wooden doors, higher rooms and suddenly 70-80,000 on top.

He snaps it up.- Or he buys it after all. Because our first plot also went to a developer in 2016, who bought immediately. They’re quick and liquid. Friday the land was online, Sunday his email: Mr...., we buy this plot. Notary is .... appointment preferably soon. ---And just like that it was gone. He paid promptly and had the money ready.

Wow, yes. Could be. Then maybe for the sellers the argument that one will build a single-family house doesn’t hold; the developer will rather exploit everything and build a semi-detached house, two stories plus a staggered floor and four parking spaces.

Why does it have to be geothermal energy? That might further restrict the choice of property, because, for example, in water protection areas, geothermal heat pumps are often not allowed.

It doesn't have to be, it was just an idea. The annual performance factor is higher than that of air-to-water heat pumps. If that doesn't work, then it just doesn't. The house or property doesn't depend on it.

Everything is more expensive than standard. Then comes the fancy bathtub, the rain shower, a few nice-to-have features in the electrics, a bay window, wooden doors, higher ceilings, and suddenly there's 70-80000 on top.

I expected it to be more expensive, but not that much. It's hard to find concrete numbers...

Geothermal heating compared to gas and solar about 15 extra cost. Clinker around 15 extra cost. Engobed roof tiles around 8 extra. And so on. I was talking about my 270 to 300 as standard.

You, when you read here and there what you want, you can conclude that the bathroom should be a bit more appealing (+10000), some little electrical gadgets (+8000?), raising the rooms (+5000?), walk-in attic (+????), etc. are obviously included for you. For me, there is the cheap standard and the somewhat better standard. Most settle for the latter, although some here already consider room height increase, KNX, and electric shutters as standard. But I don’t consider that standard. The real clinker or slate roof... wow, putting that on a bungalow roof is already worth the value of a shell construction, fewer people build that way because they prefer to spend the money on nice interior fittings or equipment from which they really benefit. Everything else is then installed in the villa area, where you certainly cannot compete with 450000.

We recently looked at a plot of land, which including additional costs is at 240000.

If you subtract the 240000 from 500000, there are a modest 260000 left.
Minus minimal secondary construction costs of 30000 leaves 230000.
That’s enough for a cheap standard house of 140 sqm with lots of electrical installations, white plaster, gas heating, and concrete roof tiles.
Outdoor facilities come later... as much as I’m sorry about that.
You really need to think carefully about what’s financially possible and what works with the distance. The house isn’t going to be given to you.
You’re probably better off with an existing property – the garden is already finished there. But you will likely have to do without your slate roof in any case.