Floor plan design for a single-family house with 165 sqm including a basement and light well

And, ask your architect for a serious price calculation. It seems that some earthworks will also be necessary. And, I seriously wonder what you want to do with so much basement space.

And, I seriously wonder what you want to do with so much basement space.

It is also obviously still within the thermal envelope (hobby room, technical room) and also has two stair accesses. Apart from that: So much basement space is great. Better to have and not need than to need and not have... But it also has to be affordable. If it should/must be a "white tub," there is not much in the way of DIY work. Then the first €100,000 are really burned on the basement.

Well ... 170 sqm of pure living space and 145 sqm of basement as well as about 10 sqm of storage space in the garage room for

Number of people, age: 2 adults (and maybe 2 children later)

is already quite far beyond "better one would have"

A visible roof structure is also a dog tax.

That’s true. We don’t have a visible roof structure, but everything is open upwards. That was, of course, due to the thermal insulation in the living area, a position costing about €5000 for roughly 25 sqm of floor space.

Where do you think I can save the most money? Besides sqm and basement.

The question is broad and wrongly posed. The most money can only be saved by reducing living sqm and by giving up the basement. Everything else is barely peanuts.
What builders can and must provide themselves are the painting and flooring works. But that is almost always borne by oneself in a turnkey house and is reflected in the obligatory €20,000 own contribution in the financing.
A living sqm costs €3000 in a standard single-family home.

and of course also help out with the construction companies. If the construction company allows/wants that.

Do you work shift work or are you not working anymore? From the side of the construction companies and craftsmen, this usually is not an option because safety (employment contract/insurance) is an important factor. For you, it would mean that the warranty could be questioned.

Wardrobe in the hallway possible?

No, I don’t see that here. It is simply not planned.

Basically we ask ourselves whether a separation between dining and living room makes sense. Or whether that then makes the rooms too small again.

Why do you want it? I don’t see such a thing as necessary. (Actually, I would be more concerned about the entire wardrobe (ideally at least 60 cm per person of closet space with 60 cm depth).

There is also a house in the forum with 240 sqm with a double garage without a basement where a sporty price range was defined. Here the builder writes that he will reach/keep the €550k.

1 out of 10 or 1 out of 100?
Doesn’t matter. I see a simple house with 150/160 sqm with a budget of €450,000. No more and no less. No basement, no double garage. Less if I see the big windows. Plus ancillary construction costs and exterior works.
€450,000 costs a house of about 150 sqm in a normally decent execution. You won’t get a double garage including a pitched roof or a basement as a giveaway.
Regarding the design:
it doesn’t impress with creativity. I can’t identify an architect, it’s as plain as it is. There are no refinements, rather the deficiencies resulting from uncreativity. See missing wardrobe/storage, poorly arranged WC sanitation on the short side, too large living area in relation to too small dining area. The fronts appear disharmonious due to the window choice. I perceive them as slapped together. And last but not least: 245 cm high windows, which appear very bizarre in narrow width, are to be installed in a storey with 257 cm height. Aren’t these some kind of fantasy dimensions? If they aren’t: where does the idea come from to design the windows so narrow and so tall? That looks totally bizarre!
By the way: I don’t understand the basement either. The technical equipment can be well accommodated on the ground floor. The slope does not make many basement rooms necessary now. I also can’t read from your needs that many hobby rooms are necessary. I mean..

Number of persons, age: 2 adults (and maybe later 2 children)
Space requirements on ground floor, upper floor: 164 sqm
Office: family use and home office
Guest sleepers per year: currently not necessary
Open or closed architecture: open
Conservative or modern building style: modern
Open kitchen, cooking island: open kitchen
Number of dining seats: 6
Fireplace: yes
Music/stereo wall: yes
Balcony, roof terrace: no
Garage, carport: double garage
Utility garden, greenhouse: utility garden
Further wishes/special features/daily routine, gladly also reasons why this or that should or should not be: light well in front of living room window for an additional office/bedroom in the basement.

There is nothing mentioned here except an office need.
Fact: the house does not fit your needs nor your budget!

Then please ask directly what was done yourself.

I personally carried out a complete renovation mostly on my own.

And, you can say that. Friends/acquaintances who ultimately gave you the approval for electrical, drinking water, and wastewater systems...
That’s actually the main problem. You can install the stuff 200% correctly, in the end a certified specialist company must sign off, otherwise the utility company won’t install a meter.

And cheap? If you can’t do masonry? A lot can go terribly wrong. Roofing? Can be deadly for an amateur.

I’m amazed. You all yell at me here when I say, "well, 3,000 EUR/m² isn’t necessary, it can be done for 2,500," and then statements like “throw the stuff on the roof yourself, then you’ll be under 1,000 EUR/m²” come up?

Absurd... Masonry, roofing, that’s the pro’s job, unless you know someone.
Inside you can let loose and that’s where the savings potential is high.

I am surprised. You yell me down here when I say "yeah well... 3,000 EUR/m² is not necessary, it can also be done for 2,500..." and then statements like "throw the stuff on the roof yourself, then you'll end up under 1,000 EUR/m²..." appear here?

Why kick a dead cow in the neck? This project is completely underfunded and I don't think anyone has recognized the purpose of this mega bunker underground yet. So back to square one.