Painting work in new construction by own effort

If you want to wallpaper over it, you should at least "sand over it once."

But he doesn't want that.

Alternative textured roller plaster (easy to connect and hides a lot) or brush plaster

A few days ago there was a painting thread at a RH in the stairwell. That's when I had the roller plaster shown to me. So: it is not what you imagine plaster to be. It then looks like woodchip wallpaper :(

I never said that I don't want to sand. For me, filling holes and sanding is not a problem. I just want to have a good result in the end that lasts for the next years (if occasional small cracks appear, that is normal, I know that, but there should only be occasional ones and not many or very many). That's why I ask whether filling and sanding is enough or if in new buildings it absolutely must be painter's fleece because otherwise the wall becomes full of cracks as the developer said (maybe he also greatly exaggerated). We have calcium silicate stone walls and no experience with them.

I never said that I don't want to sand

No one is claiming that either.
You were just advised against it if you don't want to wallpaper.

I had the cotton plaster shown to me

No, that was cotton plaster. Roll plaster is something different :-)

No, that was cotton plaster. Roll putz is something different :)

No, the OP used roll putz, , whom I asked to show me the cotton plaster, used cotton plaster. However, as far as I know, he did not upload the photo.
Just read it yourself
https://www.hausbau-forum.de/threads/rollputz-im-treppenhaus-wie-auftragen.43640/page-2#post-582265

The cotton plaster did not appeal to us visually

it would be either for the proper textured plaster, or possibly paintable plaster such as clay
or try to smooth the walls and just paint them

But it is still a question whether too many cracks will appear in these materials that will be visible