Make an in-wall cable duct yourself?

or you do it like we did. Attach the lowboard to the wall and screw the TV to the lowboard mount.
By the way, all the cables are inside the conduit. They go down into the cabinet, and the rest of the equipment is there as well.
No cables visible and my better half is/was happy.

Then I can mill a 20cm deep storage compartment for the TV magazine into my 36.5cm exterior wall.

No problem, as long as you don’t make dozens of other compartments next to it. Otherwise, the walls would collapse with every core drilling. As long as you cut vertically, it’s only a very small structural issue that you weaken the wall over 10cm width. Two rows of bricks above, the load is completely distributed. It’s different if you cut horizontally, as the masonry is weakened over the entire width.

We only want to install the flush-mounted conduit on this wall.

We don’t even have a core drilling for the exhaust/recirculation hood,

If it is important, we are building KFW 55

You really don’t need to worry about thermal bridging, since KSS doesn’t really insulate anyway, it just buffers. So the proper insulation effect here only comes from the insulation boards. But I definitely wouldn’t go drilling into the exterior wall just for a cable duct like that. ’s solution or drywall with brick slips or wooden slats as decoration and ventilation stuff like Ambilight, higher board, speakers – there are so many ways to hide cables or a surface-mounted duct... Don’t get stuck on one solution again.

it's only about a hole 6cm deep, 8cm wide and 100cm high. we actually don't want to make an extra partition 1. then many pieces of furniture (wardrobe and lowboard) would no longer fit in depth there because otherwise the terrace door would already start (currently there are still about 50cm of space between the wardrobe and the door) 2. the TV should definitely hang on the wall (75 inch) and my wife would like to have a lowboard underneath to put decorations or other things on.

HDMI wirelessly? Well, HDMI 2.1 probably can’t do that, right?

You have to check yourself.

It’s just about a hole 6cm deep, 8cm wide, and 100cm high.

We don’t actually want to build an extra drywall.
1. Then many pieces of furniture (cabinet and lowboard) won’t fit in depth there anymore because otherwise the terrace door would already start (currently there is still about 50cm space between cabinet and door).

2. The TV should definitely hang on the wall (75 inches) and my wife would like to have a lowboard below to put some decorations or other things on.

Well, if that’s "only" a cross-section of 50 cm², then just do it, why are you asking about such a small thing?

I think you’ve fixed on one solution and are now trying to force it no matter what.

A 25mm conduit (6 cm² cross-section), on the other hand, has been tried millions of times in such a wall and is relatively easy to install.

And no one is saying that you have to cover your entire exterior wall with drywall. A simple box that frames the screen with a slight overlap and is a few centimeters deep and then painted in a contrasting color is enough.

You can either let the box run continuously to the floor or so that your lowboard reaches the exterior wall at the bottom. Leave a hole open at the bottom or install an inlet with a brush seal and carry it out identically behind the TV.

There are also somewhat different ready-made solutions. You just have to fix those and push your lowboard against the wall (in that example just imagine the shelves gone and the wooden wall with more overlap).