Floor plan optimization city villa + fill consideration

I believe the OP has not yet understood that the half-turned staircase has become a quarter-turned one with narrow treads and thus in the area where the small bathroom was, there is now enough space for a bedroom.

They are simply two completely different types of stairs. In this case, however, the quarter-turned one on the upper floor results in a nicer floor plan. On the ground floor, some space is wasted – or if desired, a door to the garage is possible.

Visually, a staircase enclosed from both sides like this is not ugly. With spotlights on the ceiling above the staircase and perhaps a floor-to-ceiling window, it looks very modern.

Visually, a staircase enclosed on both sides is not ugly. With spotlights on the ceiling above the staircase and maybe a floor-to-ceiling window, it looks very modern.

I don’t find it ugly either. Here it is mainly a question of effectively using the space if you want to fulfill all the OP’s wishes. The architect really twisted himself to conjure up any kind of solution.
The "gallery" simply doesn’t exist because there is not enough space given all the wishes. But if the gallery is more important than the dressing room, something can surely be done about it.

I don't find it ugly either.

Here, the Swabian understatement sneaked in for me after all ...
"not ugly" in Southern German means "very beautiful" further north
Freely adapted as "nothing said is praise enough".

Ah yes, exactly! I was thinking of my old platform staircase. That's why I didn't understand it. What disadvantages do I have with the new type of staircase on the ground floor? There was talk of wasted space? What actually becomes smaller on the ground floor because of this? Do I still have a storage room under the stairs? I can't imagine what this staircase looks like when viewed from the ground floor. Does this staircase look better as an open wooden staircase than the masonry version? I am open to a new staircase, it just has to be child-friendly.

Well, that's a matter of taste, where presumably everyone has a different opinion. Personally, I really like stairs with crumbs of all kinds. Others find arches stupid and only accept straight steps where it always goes straight ahead. What is specifically better for children now, I don't know. I think it mainly depends on a proper railing with an additional handrail in the lower area, right?

Otherwise, nothing will be smaller on the ground floor. You could still make the storage room under the stairs. The question is whether an open hallway with an additional big cabinet under the stairs isn't simply nicer. Closed side walls look, in my opinion, really a bit better with the landing in this case than with the quarter-turn stairs.

The child-safe staircase does not exist. Children are too different for that.

Straight steps are easier to walk on, as long as the staircase is not as steep as a chicken ladder.
As so often, it has to fit and one has to weigh up.
My father, with hemiplegia, takes all the stairs up and down as long as handrails are installed on both sides.