Floor plan design and placement - Single-family house approximately 200 sqm on a 900 sqm plot

I like the staircase much better this way. I would still pull the living room exterior wall back by one meter and would have the option of a roof terrace from the bedroom on the upper floor. If you already have such an "extension." I am still not really satisfied with the corner for the shower in the children's bathroom. Maybe take another close look here at how much space is needed in the utility room and whether a 1x1m shower might also be sufficient in the children's bathroom. Maybe also a combination of both rooms or the access to the utility room through the children's bathroom? The space below with access to the garage is presumably also intended to be used as a cloakroom. Since the door to the lower WC perhaps should not be in the middle of the wall, so that a cabinet can also fit there. For a simple WC, the 5.5m2 is already quite extravagant ;-).

It will only be planned after the placement and planning of the bathroom (the currently drawn bathroom objects serve only to estimate the size and do not represent the placement in the final bathroom), but regarding drainage, there will be a good solution...

That’s complete nonsense! Yes, you always find a solution, but whether it’s "good" is relative... probably good in his eyes, but he doesn’t have to live with it afterwards.
He just makes it easy for himself. And afterwards it turns out that you’d like the toilet in the other corner and he says... oh, there? Yes, that’s possible but then we need a boxed-in area for the drainage on the ground floor or something, I don’t know. Now you can plan and move walls, so I would strongly recommend you also plan the placement of the sanitary fixtures now. The drainage of a washbasin can be shifted a bit, a toilet waste pipe is not so elegant to run a few meters sideways. Some might do it, I wouldn’t.

Aside from that, I like the version with the stairs much better. It looks more harmonious. Drainage is also easier. Do you want the long side of the "U" open or closed?

Drainage bathroom: Will only be planned after the placement and planning of the bathroom (the currently drawn bathroom objects are only for size estimation and do not represent the placement in the final bathroom), but there will already be a good solution regarding drainage....

But then I would start with the bathroom planning immediately. There is only a limited possible solution, which will not necessarily be great.

Roof terrace: Yes, in principle that would be an option. However, the extension is located directly at a street intersection, so you would be sitting there like on a plate and the street is also quite busy. That is why we decided against it.

Children's bathroom: What bothers you about it? That you potentially hear noise from the shower from the children's room? Or something else? I basically don’t think the idea of moving the shower rather into the utility room is bad either. We do not want a shower with a glass partition.

Stairs: We also really like the version, we will probably stay with the U. Our preference would be if the long side of the U is open (by that I mean the wall is half-height and rises along the stairway.

Ground floor toilet: The size is due to the fact that we want to keep the possibility open to potentially retrofit a shower at some point. As long as that is not the case, a large cleaning closet should go in there. The door can be reconsidered... You would then place it directly next to the basement stairway? So that there is maximum closet space towards the garage?

Bathroom drainage: You really scare me... Could you elaborate a bit more? What would be the "one" possible option? And why is it not really great? Without going into details of the planning it would probably be the idea to accommodate the sink and toilet on the right side under the door and on the left side a walk-in shower and a nice tub (corner tub, whirlpool tub or something like that). Is the potential problem only the toilet’s waste pipe? Or are there other issues? I think I don’t quite understand the core of the problem yet. What would be your suggestion then? Swap bathroom and dressing room as the only reasonable option? Or is there also a sensible solution in the current form?

And why isn't it really great?

Because somewhere under the bathroom a 20 x 20 cm boxed soil pipe will be visible in the hallway.
It's best to plan such a thing in a wall closet or an adjacent room/storage room/guest WC, which is planned under the bathroom.
And the closer this soil pipe is at the top to the toilet and with few bends, the better, because it then more likely avoids a blockage.
Since the walls don't even align in your case, it will be quite difficult to install a soil pipe without it being obtrusively visible somewhere.
2.75 bathroom depth… minus door leaf 1.70 remains for your toilet (1 meter width) and 70 cm for the washbasin.
Corner bathtub also needs to be liked - it's not exactly modern now ;)

We are planning a built-in wardrobe / built-in coat rack on the wall to the right of the entrance door. Would that be a good place to accommodate it? Is the problem only the visibility of the downpipe, or also that the dishwasher noise is very loud if it is not somehow enclosed separately?

But that sounds like swapping the dressing room and bathroom would not solve the problem, it would then also be above the office, just like it is now. What would be a possible solution then?