Floor plan and elevations for a single-family house of approximately 160 m² on a hillside location

I know the warmth from wood well enough. Yes, it is a different kind of warmth. It also requires more work than just turning on the thermostat.

when do you ever need it to be 3-4 degrees warmer quickly in the evening?

We decided against it and never regretted it. Although or precisely because we know heating with wood and have our own forest. Even houses from the 70s and 80s, before energy efficiency classes and Tupperware insulation, are often way overheated for us in winter. Modern houses don’t cool down so quickly, there are no drafts, far fewer thermal bridges, the perception of warmth is different. It is subjective and everyone has to decide for themselves. For 10,000 euros you can also get a nice piece of a photovoltaic system.

I know the warmth from wood well enough. Yes, it is a different warmth. It also takes more work than just turning on the thermostat.

when do you ever quickly need it 3-4 degrees warmer in the evening?

...
It is subjective and everyone has to decide for themselves. For 10,000 euros you can also get a nice piece of photovoltaic system.

And you can also run it at 1 degree higher room temperature for that.

Whether you think that’s great and what it’s worth to you is up to each person/is subjective. But to connect this to the thread here, the simple question is whether there is budget left or not... and that’s why this thread is stalling here.
The majority (or all?) of the active users in the thread say you can’t get the design done with the stated budget. For that, the OP would now have to clearly state whether the budget is still flexible.
From the statements so far, it seems to me that overall there is still a lack of feeling for how much everything around it costs in euros. That’s why I cautiously asked about the garden and landscaping contractor. But I might be mistaken.

In any case, I don’t think the floor plan discussion will move forward as long as this remains unresolved.

when do you need it quickly 3-4 degrees warmer in the evening?

We do every evening.
We have the heating set to 20 to 21 degrees. That is usually fine during the day, but too cold for us in the evening.
Even the piece of photovoltaic that I could get for 10,000 euros (if I could buy it now) wouldn’t help me much.
But as you say, it’s subjective.
I didn’t want to start a discussion about it either. Everyone simply has their own opinion on it.

Uh, that would be way too warm for me. No matter what, has too many wishes for his budget. A fireplace must also be discussed. I don't necessarily see a basement with that slope. How much leeway does your budget have upwards?

We are considering the basement alone because of the hillside location.

You are filling in the entire slope at the back anyway. What difference would the basement make there?

On the ground floor, there is then a generous living and cooking area.

And yet the kitchen is tiny, the dining area is long and uncomfortable, and the chill-out corner is rather small! Even if it’s not noticeable at first glance, for me this is probably the worst planning you can do. A lot of square meters used up and in the end still no space. The guest shower on the ground floor is rather too big for that. Upstairs there are two more showers – are those even necessary? The kitchen pantry is also inefficiently wide – as a utility room with washing machine, access through the kitchen would be completely unfortunate. This leads directly to the point that the laundry would be well placed in the basement, but at least a laundry chute should appear somewhere. The drainage of the basement has already been mentioned as a critical point – I would also be interested in the solution. The space wasted for the chimney on the upper floor is also record-breaking. Also absurd are the galactic excavations around the house for the light wells. Who wants to live in a garden where you constantly need a fall protection? That costs a lot of money and is ugly as night in the end. The terrace is raised artificially and squeezed halfway behind the garage because everywhere else it slopes steeply downward. Honestly? I would crumple this up and throw it away. I don’t see any site plan with measurements, building envelope, and whatnot, so one can only speculate about alternative options: If it were mine, I would plan a larger footprint to meet the desire for 4 bedrooms + bathroom + master bath upstairs. Accordingly, the cramped space on the ground floor would relax and the technical room would fit in. I would eliminate the basement and rather consider expanding the roof, maximizing the roof pitch. There is light here without fracturing the garden, and you have to pay for the roof anyway. The hobby mega room will be cut due to budget constraints. The two offices move into the roof and there might also be space for a storage room. End. I would plan the heights for the terrace and access path precisely so that I have to raise as little as possible at the back and dig as little as possible at the front.

So. The children are in bed and I can respond. A few topics have actually accumulated by now. Thanks for the interim feedback. I will try to sort it out:

1.) Budget and cost framework:
We are currently planning with a prefabricated house and have so far obtained two offers for turnkey houses based on our (fundamental) wishes. Conditions were: upper floor with approx. 80 sqm and 2 bathrooms, ground floor partially set back with a shower bathroom, cellar usable as living space, fireplace, photovoltaic system + storage, air-to-water heat pump. So in terms of area and main cost factors exactly as the architect planned. The result was the mentioned 650,000 - 700,000. We want to do the garage ourselves. It is not included in the costs. We also want to do quite a bit of the interior work ourselves (with a friend who is a reinforced concrete builder), so that the offered turnkey house costs will be reduced somewhat. Our budget depending on the current interest rate is about €750,000, so we assumed that the house including garage is within budget. We still expect the precise evaluation in coordination with the architect. Since I didn’t see this as a big problem at all, I had not described all the details of self-performance and previous offers in detail so far.

2.) Fireplace:
This was discussed extensively and it is interesting to know the pros and cons. For us it is a "nice to have". We might omit it.

3.) Plot:
We are not quite satisfied yet with the current planning regarding the new elevation profile, because the terrain still slopes down from the street to the house. We would like a slight incline up to the front edge of the house. Then we imagine that the terrain on the side next to the cellar windows slopes more steeply than before, so that at the rear cellar window and at the rear side cellar window we no longer need any light well. Then a horizontal terrain profile at medium terrain height between the back of the building and the rear property boundary. There would then be stairs from the terrace down to the garden and a planted slope. The height difference would be about 1.20 m. We want to discuss this matter next with the architect. Since we only wanted to discuss this with the architect first, I also wrote that the outdoor area is still unclear and should be planned in more detail. But maybe you can already say what you think?
It was important to us to have a horizontal level at the back in the garden. As it is now, we would have to fill a lot. Since we think the budget is sufficient, we want to keep the cellar as is.