Mold problem in new kitchen - how to prevent it in the future?

The vacuum insulation panel would be completely unsuitable and the worst end.

I only mentioned the perimeter insulation because it often has a poor WLG in hardware stores and absorbs little moisture.
It is not primarily about the insulation, but about the moisture transport to the outside. Without knowing what kind of paint is on the wall.

Provably, CalSi and HWL would work, only they are rarely found in hardware stores.
Possibly a perimeter insulation would fail, I better withdraw that tip because I assume that the distance according to the manufacturer's specifications should be sufficient :)

When was the room plastered?
I also think it is most likely due to the uninsulated wall combined with the location of the refrigerator without air circulation. However, I find it almost remarkable that there is so much water that it runs out from under the fridge.

Well, provided the device defrosts properly and has no defect. Otherwise, the kitchen planning was suboptimal without the necessary clearance.

The room was plastered last year in June/July, so a little over 6 months ago.

I would rule out a device malfunction, the fridge/freezer unit is now (without a built-in cabinet) positioned in the middle of the kitchen and is in operation. No water is leaking anywhere.
The wall behind / beside the refrigerator was covered in water droplets, as if those spots had been sprayed with a spray bottle. By the way, also on the inside, so between the appliance and the built-in cabinet there were these droplets.
That is no longer the case now, neither on the appliance nor on the wall.

Then the location and the lack of distance and the cold exterior wall are probably really the cause.

As an "active" solution, I see two more possibilities besides the insulation:

1. Install an extra heater in the corner to warm the corner (which usually also increases air circulation).
2. Install a small fan in the ventilation slots to create faster air exchange.

They are crutches, but are regularly used in other cases ...