Renovating an old building, which insulation is suitable for the exterior wall and possibly the basement

Mold has nothing to do with subsequent insulation. Mold occurs when moisture condenses on cold surfaces. Mold is therefore (usually) related to incorrect heating and ventilation behavior. Only in exceptional cases due to construction defects.

Connection to the insulation black walls had, therefore I wanted to gather impressions

It is not due to the insulation (regardless of the type). After insulation including new windows, the house is tighter than before with drafty windows. If it is not ventilated, mold can develop. This also applies to new buildings.
It becomes extreme when drafty windows are replaced by new and tight windows. If it is not ventilated then, the humidity has to go somewhere or condense. And cold exterior walls, preferably in the corners, are suitable for this.
If mold appears after proper insulation, almost 100% of the fault lies with the biological component, namely the occupant.