Build over gas, water, electricity, and telephone lines with a garage?

In general, insulated garages with poor ventilation tend to experience condensation in summer. A reliable design is an uninsulated and well-ventilated garage.

Topic floor slab: If only paved, the horizontal waterproofing, which is usually welded onto the floor slab, is missing. This will cause the humidity to be permanently higher. How big the "problem" is depends on the soil conditions and how well your garage is ventilated. However, you could of course install a vapor barrier as a foil under the paving; this would probably be an equivalent solution.

These are already very good tips and suggestions from you. Thank you. We will now first wait for the [Kostenvoranschlag] and meanwhile consider what can be done for sufficient ventilation.