Here is a small update:
The house is apparently just about to be sold (for the requested €550,000) to another family who then want to use it 100% privately. The building authority has apparently agreed to this as well.
According to the real estate agent, the potential buyers want to clear the garden without consulting the nature conservation office and convert it into a normal lawn area with a regular fence, etc. "The authorities don't pay attention to that. They are so overwhelmed. In practice, nobody cares." The agent and buyers seem to be okay with this.
I find all of this somewhat very suspicious.