Floor plan for 200 sqm city villa - Are wishes achievable?

A straight staircase would appear less obstructive and would later allow for an elevator.
So, your statement @11ant more or less means:
1) Either leave it as is and accept the compromise or
2) Redesign everything so that the straight staircase fits differently?

Either 3) leave it as proposed by the contractor or 4) not redesign, but newly plan with a straight staircase. I am against 4) but also not for 3), because unfortunately is right.
An elevator would also need clearance at both ends, which you do not have here at the starting point. What an elevator does not need, however, is a perfectly straight route—preferably more width. But retrofitting "age-appropriately" is anyway a matter of the age when building—unfortunately, your settings do not allow a view into your profile.

No cat litter box needs a 9 sqm bathroom. And I know how much space a large litter box requires. I had a petite 8 kg chunk myself, for whom pretty much every cat litter box was too small.

The whole floor plan is so unbalanced. I’m just going to refer to your design now. Size isn’t everything. Huge bathroom, cramped hallway, cramped wardrobe only after the bathroom and the stair landing. That means the dirt is already spread and you walk through snow water, street dirt, etc. in socks or slippers.

The kitchen is simply big. Unergonomic with a cat table. I don’t know anyone who uses the table in the kitchen for eating. For most people, it’s cluttered. You have a large one in the open-plan area. The days of the formal living room are basically over. In my opinion, the bay window doesn’t lighten things up. It just unnecessarily splits the terrace. The kitchen belongs to the terrace, where usually quite a lot of time is spent and which serves as a dining area and living space in the summer half-year.

Upper floor
Bathroom—is that the one with the sauna? It also contains a space without added value.
Children’s room is cut up by the bay window and looks somewhat like Tetris.
Why this narrow strip by the stairs?
You have so much space. Remove the bay window, straight stairs.
Parent’s wing. Accessed through the dressing room. Get up, grab clothes and out. Forget something, no one is bothered, turn on the light absentmindedly, no one is bothered.
Office, wow, big.

Basement—don’t forget the light well for a second office.

I see the 550,000 as insufficient. The basement is in living space quality and the bathroom probably won’t be Ideal Standard either.

I would remove the bay window at the entrance. Straight stairs, spacious hallway (yours feels cramped), wardrobe by the entrance, maybe reduce the bathroom a bit. Kitchen to the terrace and more ergonomics which will probably lead to a reduction in size.
On the upper floor straighten the wall of the children’s room and give more space at the stairs. It’s still more than big enough. Remove the wall in the children’s room. The children’s room will be rearranged and redesigned countless times anyway.
Design the parents’ area differently and put windows in the dressing room.

I also have 200sqm of living space with a straight staircase, but without a basement. It definitely works more harmoniously, with smaller rooms yet still appearing spacious. The designer's draft is clearly a joke! No direct access from the kitchen to the dining room?!

your rooms are completely oversized.
200 sqm is indeed large, but a guest bathroom of 9 sqm, a kitchen of 28 sqm(!!) a children's room of 25 sqm and a main bathroom of 23 sqm(!!!) no one needs that.
When you furnish the rooms it looks like it was thrown together

Yes, I also find the guest bathroom quite large.
If you reduce it, it only helps the straight staircase for now.
A sauna was actually planned in the main bathroom. I think as it is planned in our design, it is anything but "large." Since a lot is put into it, the sauna can only be quite small, otherwise the bathroom becomes too crowded. Or we will forgo the sauna after all.

Up to my 11th year of life, I had a similarly sized children's room and found it wonderful. After that, it was only 11 sqm and that was manageable too. If it's included, we would of course like to enable it; for a child, that is really something nice.

Something about the kitchen:
We currently have 22 sqm. It’s not supposed to become an open kitchen plus seating area.
Our current kitchen doesn’t have a proper seating area, only 2 bar stools at the island, and it actually looks anything but "empty."

I understand what you mean, but somehow the experience from our current apartment says otherwise.

But "age-appropriate" modifications are anyway a matter of the age when building - unfortunately, your settings do not allow a look into your profile.

What do you want to know? I'll have to take a look at what I need to change in my profile. We are both in our early 30s, but of course you want to live in a house like that as long as possible.

That means the dirt is already spread and you walk through snow water, street dirt etc. with socks or slippers.

You are probably right

The kitchen is simply large. Unergonomic with cat table. I don't know anyone who uses the table in the kitchen for eating. For most people it is cluttered. You have a large one in the open space. The times of the good parlor are actually over.

What are you referring to with unergonomic?
Do you find the work paths so uncomfortable?

Oh actually we always used our dining area in the kitchen (breakfast and dinner) as long as our daughter could still sit in the separate chair including table next to it.
Unfortunately, that is no longer possible because she now sits directly at the table and that is too high at our block in the kitchen.
I actually find it much more practical not to always carry everything from the kitchen to the dining table.

Upper floor
Bathroom is the one with sauna? also contains room without added value

Do you mean the sauna has no added value? Or how is the sentence meant?

Stairs for what is this narrow edge

That would be air space