Fence construction / Contact details of adjacent property owners

Whoever wants the fence builds it on their property (with the prescribed border distance and otherwise in compliance with local regulations) and pays ... it's that simple.

Unless it is regulated by law, ordinance, statute, or development plan who must install a enclosure (if required).

To keep it simple, I recommend reading the [Landes Niedersachsen] on neighborhood law. There you will find all the claims you can make (at the moment unfortunately none at all, since the neighboring property is not developed). So the only option is the fence on your own property, although the future neighbor could still demand a shared enclosure on the boundary.