As a construction expert already says, it clearly depends on the expert and in my opinion, their assessment should always be valued higher than what can be said from behind a keyboard. It also depends, among other things, on the construction of the cellar and the expert will have already seen that. Also, whether the moisture can even come from outside – which, according to your description, is doubtful if it also occurs on interior walls.
There are also several options for you (depending on the actual damage) that the expert should explain to you including a cost estimate, so there is little point in discussing costs here.
I still suspect (with all due caution) that the problem can be solved on its own or with new plaster and paint if the room is used properly in the future. There is also the possibility of installing a ventilation system that adjusts/controls according to the humidity.
Regards Dirk Grafe