Cost of a central air conditioning system in new construction

In a properly planned new building, there should be sufficient heat/sun protection so that no air conditioning is necessary.

Yes, there are more than a dozen "buts." Since the Energy Saving Ordinance and various KfW levels have existed, things have not improved regarding indoor temperatures in houses during summer. In winter, yes, everything is great. Modern construction saves a lot of primary energy. Political goal thus achieved. However, the effect is also present in summer, and after a few days even the best shading no longer helps. If tropical nights are added...

The location is Germany, not Spain, Italy, etc., right?

Yes, for that reason, air conditioning in Germany does not run continuously for 3-4 months as in Southern Europe but only for a few weeks or sporadically in midsummer.

Air conditioning also has (high) running costs.

That used to be the case. Start/stop systems are no longer really installed. Rumor has it that half the forum heats their houses with the devices in reverse mode, and the operators enjoy pleasantly low operating costs. The additional 200 euros per year for active cooling can be managed, I think.

In a properly planned new building, there should be sufficient heat/sun protection, so that no air conditioning is required. Namely, venetian blinds, roof/facade insulation, roof overhang, etc.

Well then, have fun with a KfW 40 house with top marks in the blower door test.... During a prolonged heat period, heat enters through door opening, ventilation, etc. And if, as mentioned above, the house can no longer cool down at night, then you have a long time to enjoy the KfW 40 standard.

... and if you also have a nice wooden post house, it will follow the outside temperature with the best shading in 3-4 days. Have fun with that.

Cooling (keeping) only works through mass or cooled air. With today's papier-mâché houses, only the latter remains.

Most air conditioners can also heat. Depending on the system, it is even considered a form of renewable energy… During the time the air conditioner is running, the sun is also shining. Thus, the photovoltaic system provides the energy.

I have tried to educate myself on the topic of central air conditioning and found surprisingly little information on the internet about exactly how and with which devices this can be realized.

If I understand correctly, you need appropriate piping in the house and a refrigeration machine. Are there concrete examples of such devices? On the internet, I find a lot about split and multi-split systems, but hardly anything about central units. If I understand correctly, the refrigeration machine can be installed in the basement. How is the heat then removed?

And how do central air conditioning systems and controlled residential ventilation devices work together? Are the ducts for controlled residential ventilation and air conditioning installed separately and then do the two systems operate independently?

surprisingly little information

Because this is more common in commercial buildings and not just anyone has the experience there.

How is the heat then removed?

Through evaporators in the ducts.

how do central air conditioning systems and controlled residential ventilation devices work together?

Basically not at all in residential construction. As you have noticed, both are installed side by side and operate independently; at most, some kind of integration takes place at the highest level.