Basement cinema - Sound insulation

Lignotrend is certainly the luxury solution here.
A reasonable floor construction in combination with a drywall stud frame and a suspended/sprung ceiling will certainly do as well.
Create about a 100 mm cavity on the exterior walls with wood or metal stud framing, insulate it with mineral wool, and then triple-board it; for the optimal result, use a mixed boarding with Knauf Diamant 12.5 on the outside. Something similar on the ceiling, additionally suspended or with a spring rail, depending on how much space you have upwards.
Room acoustics will certainly become an issue then, you might have to optimize the reverberation times.

A reasonable floor construction combined with drywall stud framing and a suspended/sprung ceiling will certainly do the job as well.

I have underfloor heating; the entire basement is covered with tiles and skirting boards.
What exactly do you mean by the floor construction? I have to consider that the door opens inward and that it is a concrete-set steel frame.

Create an approximately 100 mm cavity at the exterior walls using wood or metal studs, insulate it with mineral wool and then plasterboard it three times; for the optimal result, use mixed boarding with Knauf Diamant 12.5 mm on the outside.

Won't impact sound be transmitted again through the stud frame? It probably won't help much against bass, right?

Something similar on the ceiling, additionally suspended or with spring rails, depending on how much space you have upwards.

The room is 2.4 m high.

Room acoustics will certainly become an issue then, maybe you'll also have to optimize the reverberation times.

Certainly, the measurement and adjustment with absorbers and diffusers will come afterward, but the absorbers can already be planned at the early reflections.

Isn't structure-borne sound transmitted via the stud frame?

The stud frame must of course not have a direct structure-borne sound bridge to the exterior wall, otherwise everything is pointless. You are basically building a multi-layer wall. Ideally without a structure-borne sound bridge or connected with permanent elastic material.

I have underfloor heating, the entire basement is covered with tiles and skirting boards.

Is the screed laid continuously at the door or with a joint? Is this joint also permanently elastic in the tile? Horizontal structure-borne sound through the floor is generally rather secondary.

The screed and the tiles are permanently elastically separated, to the anteroom... lucky break.

How do you make a wooden construction that has no vibration-transmitting connection to the wall?

I always think of the black rubber mats that you put under a washing machine.

How do you make a wooden construction that does not have a vibration-transmitting connection to the wall?

How do you build a drywall partition?

How do you put up a drywall partition?

I've never done it before. There's always a first time, and it won't be that difficult.