As already mentioned: measure and compare infrared thermometer and wall temperatures.
The building expert already did that last winter. In his opinion, no special irregularities except for the high dew point (which, however, is not unusual for exterior wall corners).
Several unfavorable circumstances coincide in our case:
1. Bedroom as the tendentially coldest room with direct access to the two most humid and warm rooms of the apartment (bathroom + kitchen). Result: humidity automatically migrates into the bedroom due to temperature differences. Measure: exhaust hood in the kitchen and bathroom fan in the bathroom.
2. Additional humidity is produced overnight in the bedroom.
3. Two of the four bedroom walls are exterior walls and the corner of these two exterior walls is the coldest spot, so humidity condenses there quickly.
Therefore, the idea is to lower the dew point by additional insulation from the inside so that humidity no longer condenses on the exterior walls. Execution, of course, by a professional.
And place the hygrometer for control.
They have already been standing in the bedroom, bathroom, and kitchen for 1 year. That's why I also know that the humidity in the bedroom never permanently exceeds 55%.
Is there the possibility of decentralized ventilation? Especially because the exterior facade would be affected? There are devices with heat recovery.
That's clear. Either single units, which are never powerful enough (e.g. Bayernventilator), or decentralized residential ventilation, which would then have to be installed in all rooms throughout the apartment. Cost approx. 7-9 thousand EUR.
Therefore, like the calcium silicate board insulation, it would rather be a last resort.
Under the given conditions, I would not cover such a wall with anything that is not permeable. We know nothing about the building envelope. I would renew the plaster at affected areas, mycelium is in the wall and not on top, and afterwards paint lime paint on the bare plaster. The tenant would also have to be obligated here; otherwise, he might end up decorating with latex paint.
The specialized company would certainly remove the old plaster at the affected spots beforehand and then plaster with the new insulating plaster. Therefore, in my opinion, there is no risk that the mycelium remains in the wall.
We would then, of course, make painting with lime or silicate paint mandatory in the lease agreement.
Well. To be honest, I am a bit at a loss too. I actually do not want to commission another expert because we had rather bad experiences with the last one (appointment duration 15 minutes and bill 400 EUR). I have now called a renovation specialist company. They will come in the next few days and then make a cost estimate. Let's see what they propose.