Indirect lighting in new construction, build it yourself

Not all stay cold.

Few remain reliably cool. Good tip!

so you can conclude that indirect light with LED strips is only possible with baseboards under the ceiling or if you hang the entire inner ceiling down and leave a gap on the outside for the LED strips

There are certainly other ideas to get creative. Let yourself be inspired from the field of interior design.

otherwise you would have to use floor lamps, uplighters, etc.?

Look at solutions from lighting manufacturers who place great value on innovation and design. There are many more variants. Behind a sofa, for example, we create optionally indirect and/or direct light with a "Stereo" from less-n-more (our favorite lighting manufacturer), in another place there is a "Jules" or a "YLUX," both the latter with battery and thus very flexibly usable. Further inspirations: Tobias Grau Flying pendant light (50/50 direct and indirect), Artemide Surf (indirect lighting hanging from the ceiling), Occhio Sento (switchable light direction up, down, both) or Lumencenter Foliage (diffuser and indirect lighting in combination)...

And keep in mind that indirect lighting requires significantly more lumens than direct lighting (Beim Leuchtmittel)

And remember that indirect lighting requires significantly more lumens than direct lighting (at the light source)

Therefore, feel free to overdimension a bit and use an adjustable driver. We laypeople usually lack the imagination to convert lumens into room lighting.

Eh 2.35m in the new building?! Are you sure the ceilings are not dropped? Or is this about a basement room?