Is ceiling heating possible as an acoustic ceiling?

That is all wrong. You have seen my own plans. And calculate not with 75mm, but with 50mm. With no more than 30 degrees supply temperature, you will get sufficient performance.

And again: LET THE HEATING BE PLANNED EXTERNALLY AND DON'T TINKER WITH YOUR IGNORANCE YOURSELF

I can’t calculate with 50mm, since my screed system only allows 75 or 150mm.
This has already been partially calculated by the heating engineers and screed layers and only once did it come up that maybe the bathroom could be a problem, although there, even with the bathtub and shower omitted, the heating load per m² is lower.

No, that's actually not the case when furniture is added.

There is not much more than a sofa, plants, and a shelf.

And acoustic panels are not 10cm thick either. You get by completely with 3-4cm. So only slightly thicker than normal pictures.

But that only dampens the high and minimally the mid frequencies.
Good for an office, rather bad for a living room with music and stuff.

I can't calculate with 50mm because my screed system only allows 75 or 150mm.

Badly planned...
You probably have to staple and go with 50mm after all. The simplest solution.

There's not much more than a sofa, plants, and a shelf.

Then the ceiling alone won't help you. A planner has to get involved.

Only calculating the room's own resonances (room modes) and then using appropriate absorbers or Helmholtz resonators helps against low frequencies. And that should preferably be done by a room acoustician, yes.

Poorly planned... You probably have to staple and go to 50mm. The simplest solution. Then the ceiling alone won't help you either. A planner has to take care of that.

Poorly planned? Unfortunately, I don't know of any thin-layer screeds that can be freely stapled.

I unfortunately don't know of any thin-layer screeds where you can staple freely.

Then just use a thin-layer system with a 50mm installation spacing. You really are hard to understand. The market is full of them. For example, the panel from Fördertherm. And use a 16mm pipe, not those small tubes that are often offered otherwise. The construction height without covering is then 22mm. It's really not that difficult to build a proper heating system. Don't do it yourself, but find someone who plans it. How many times do we have to tell you?

Poorly planned?
Unfortunately, I don’t know of any thin-layer screeds that can be freely stapled.

P.S. You wrote in the other thread that the extension is just being built. Then I emphasize my statement "poorly planned" even more if you can only install a thin-layer system now and therefore have problems with the heating. Why would you plan such a new build without proper heating planning?