Installing air conditioning --> KFW funding gone?

What about simply operating the thermal insulation in front of the windows (lowering the roller shutters) and providing some planting in front of the patio door? That is actually the common practice. It has proven itself for centuries. You don't always have to come up with technology that makes the purpose and implementation rather complicated.

Sure, but remember that slightly thicker pipes need to be laid there.

I believe this is about a split air conditioning system and not a chilled water air conditioning system; for the latter, you have a separate line (liquid, gaseous) for each indoor unit.

I am currently considering preparing the bedroom, children's room, and office. The living room adjoins the utility room; something can still be done there later...

We have one outdoor unit and 5 indoor units. What costs the money is the outdoor unit; the indoor units cost practically nothing in comparison. Therefore, you can install them all at once.

Of course, and I didn’t mean this air hose either, but the cables are overall quite a bit thicker than, for example, a power cable.

That's correct, I believe they were around 5cm and 3cm with insulation.

So with us, the slots were about 8 cm wide and 8 cm deep overall. That already means a considerable piece of wall is missing, and the breakthrough was also about 10 cm in diameter.

Experience shows that a 50 mm HT pipe is sufficient to get everything through for an indoor unit.

That is actually the common practice. It has proven itself over centuries.

However, houses were built differently centuries ago than they are today. Either the walls were so thick and the windows so small that the sun stayed outside, or the walls were so thin and permeable that air exchange happened quickly. Insulation panels that were supposed to keep the heat inside were also nowhere to be found.