Hang the ceiling using an acoustic ceiling to avoid noise.

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There are many possibilities. Most acoustic ceilings are more suitable for offices. It gets tighter when it comes to nice/discreet. We have acoustic ceilings from Lignotrend (white fir) throughout the house. It was a great decision. It looks great and above all no sound problems. We only have hard surfaces (glass, concrete, asphalt...). Guests always notice the pleasant acoustics. also has the Lignotrend system. Since you want to lower the ceiling anyway, the additional cost is not so "extreme". Substructure and installation are more complex. Best to use a good carpenter. But no drywall, spackling, wallpaper?, painting ... The system also has flush-mounted LED strips. I did not want a grid ceiling or perforated ceiling in the living area. You can see pictures in my construction thread.

In my opinion, this is more something for the public area and/or offices and less for the private area, right?

No, especially if you want to achieve good playback at home with many hard surfaces (however, I have no idea what your standards and audio equipment are), you should acoustically do something. Just think about how many hours you use the room for that purpose! Room acoustics is definitely not for beginners if it is supposed to work. There is a lot of literature about it, but without measurement technology and proper planning, it will be more than just random hits.

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... and I believe also for and - but for a comparable house size, if I remember correctly, rather for .

Room acoustics, however, is definitely not for beginners if it is to work.

However, there are only general / blanket solutions available off-the-shelf for the rough scale.

For acoustic optimization, it is not about music for me, but purely everyday living quality. A room with echo and harsh reflections is simply extremely unpleasant. We have a ceiling height of nearly 7 meters and no feeling of a church. Music comes from rather simple HiFi from Atoll, Naim, Triangle, JM Lab. High-End was once and is over.

In the home theater, we have the Knauf Cleaneo. It is also available in a more modern design than usual in offices. We also looked at Lignotrend, but with the low ceiling height (250cm) in the basement, it felt too oppressive for me. However, in the right room, I would definitely tend towards the Lignotrend, also because I prefer wood over gypsum. But in any case, it makes sense to deal with it even in private buildings. Unfortunately, I can't give you any experience regarding before and after, as we implemented this directly during construction, and even then the difference was very noticeable.