We use the appliance as a tumble dryer. As soon as the set humidity value is reached, the dryer part (compressor?) switches off audibly, but the fan continues to run. I also find this very annoying, but it has been like this since the beginning, so I think it's normal.

We have a measured humidity of 60%. The unit is set to 30 %. But only the fan is running, no dehumidification. What is going wrong?

It has to be like this. The fan provides the air flow that takes the moisture out of the room, the walls and the damp objects. The air humidity is measured in the inflow area of the fan. As soon as the air humidity has risen above the threshold value due to the circulation without a compressor, the compressor switches on again. Without a running fan, a meaningful measurement of the average humidity in the room is not possible.