Bathroom ceiling moisture + inadequate insulation

The ceiling was/has been opened for repair and left open for inspection, the warm air from the living area rises and condenses on the underlay membrane, which only stops once insulation and foil close the hole again, that's why it is now soaking wet

Also put a hygrometer in the bathroom yourself to get a feel for the humidity.
Constantly above 70% poses a risk of mold.

No, being airtight is not disadvantageous there. In the pictures, no error can really be seen. Whether the drywall or ceiling spotlight is airtight or not is irrelevant, as the drywall does not represent a sealing layer. The most common mistake (but there can be 100 other causes) is the user. No controlled residential ventilation is already very bad – if the bathroom is not ventilated thoroughly by hand consistently after every shower, morning, evening, and midday, that can already be the cause.

However, the builder already made a mistake beforehand. Because they are indirectly obligated (building according to the state/rules of technology) to create a ventilation concept according to DIN 1946-6. If they did not explicitly inform the buyer that this is missing, they can be held liable for later damages. It cannot be expected of the resident in new buildings to ventilate sufficiently themselves. A ventilation concept would have shown that a decentralized ventilation or a controlled residential ventilation is necessary. Even window rebate ventilators are not sufficient here.