Insulate utility cellar or not?

The staircase is to be a concrete staircase (landing). From the hallway on the ground floor, it then leads openly upstairs to the upper floor. The descent to the basement is to be hidden behind a "normal" interior door.

What exactly does "closed staircase" mean? Isn't it enough to have an insulated door to the basement on the ground floor?

yes

well, open staircases are in fashion right now, nice wooden stairs, airy, continuous upwards. that's how we have it. how do you want to realize a door to the basement?

Without airy and continuous, at least downwards.
Or airy and continuous, the insulating door/wall then comes at the bottom.

Although in new buildings basement rooms are also insulated from the outside, keyword dew point shift, even if only a few cm thick.

Although in new buildings, utility cellars are also insulated from the outside, keyword dew point shift, even if only a few centimeters thick.

Are they still thermally separated from the ground floor then? So slight external insulation of the cellar + ceiling insulation of the cellar against the ground floor?

In our renovation, the basement will not be integrated into the thermal envelope. What we need: insulated basement ceiling (in new buildings probably from above under the underfloor heating), insulated door to the basement, the stairway above the basement stairs will be insulated from below, insulated side walls of the basement stairwell. I don't think you can use the controlled residential ventilation for uninsulated rooms.

Are they still thermally separated from the ground floor then? So minimal external insulation of the basement + basement ceiling insulation against the ground floor?

Yes, absolutely!