We had no mold in our house during the drying phase. But we had no rain. I would probably insist on replacing the drywall and consulting an expert. Especially with the [Holzständerwerk] I don't joke around.
Our shell construction had also started to mold back then. The heating was not running yet and the expert said it either had to be urgently installed now or heaters had to be set up. At that time, the mold itself was not really serious or without consequences. The developer did not take care of it and in the end the entire drywall had to be redone...
I would also initially go up in arms. An acquaintance with a solid house received the screed in early/mid January, due to the damp weather and the lack of heating they also have an extreme mold problem. They had to wash the plasterboards daily with a mold remover, get dehumidifiers and will only be able to start the tiling work this week.
I expect my house to be mold-free from the start and to remain so. If the weather is unfavorable, you just have to deal with it. This is solved with communication and money. Whose money ––> see communication.