What is necessary and what is not always depends on your expectations. In our new build, we also did not choose the usual route of sanding everything super smooth. We have a small child and did not want to sink 20k into painting work if there is a chance that toys will fly against the walls, a Bobby car will crash in, or the walls will become acquainted with crayons.
However, you can also see that we simply wallpapered and painted on Q2. If you look closely under certain lighting conditions, you can see unevenness under the wallpaper. You have to know if that bothers you. We rarely stand in the hallway and look at the wallpaper.
It’s the same in the old building, everything depends on your expectation and on what’s underneath after removing the old wallpaper. I used to mostly just remove old wallpaper in old apartments and wallpaper over it. Nowadays, there are wallpapers called "Vliesfaser," which we used and find pretty nice. They come in different textures. I can no longer see the classic woodchip wallpaper that hangs in every rental apartment, so we chose other patterns. They also come in different thicknesses. Depending on the condition of the wall (how smooth it still is), you can choose more strongly textured wallpapers that forgive more unevenness. Very thin, such painter’s fleece, I would really only wallpaper on very smooth walls. If you have unevenness beneath painter’s fleece, the thin wallpaper above will visibly bulge and visually amplify the effect tenfold. You can imagine it as a small "wallpaper tent" spanning over a plaster crumb. The crumb itself might have been 2mm large, but the wallpaper tent then stretches over 1cm.