Purchase of land with an old barn that is also used by the neighbor

It’s not possible, we want to build 2 houses on the property, which is easily doable in RS with the building authority, etc.
House 1 next to the neighbor’s semi-detached house and House 2 standing alone at the back of the property.

The barn definitely has to go ;)

Well then, think about something to preserve the neighbor’s barn.
Just because you suddenly come up with the idea to divide the property and build twice on it, he doesn’t have to do anything at all...

Well then, think of something to preserve the neighboring barn.
Just because you suddenly come up with the idea to divide the property and build twice as much, he doesn't have to do anything at all...

The barn must also be removed with single-house development on the property.
And even if I could leave it standing, it would be a no-go to leave it standing at the current m2/prices. The barn was probably cobbled together from wood and masonry between 1930 and 1960.

I would pay him for the preservation myself, but the question is whether he is on board or not. Because one can assume that maybe his barn roof/tiles might also need to be renewed - then he would also have a "added value."

I believe we are talking past each other. If the barn was built legally and everything is in order, then you have the problem, not your neighbor. You want to build, I understand that. But you must ensure that his part of the barn stands safely. If you cannot guarantee that, then in my opinion, construction will not take place, if in doubt.

the barn is separated by a masonry = property separation.

Before the drawing came, I couldn’t make sense of the post // headline at all, what kind of question this is now.

Since today I drove past several villages with almost such double houses, always a double garage at the back, courtyard in between, garden behind, I understand the property ;)

It doesn’t work, we want to build 2 houses on the property which is easily possible in RS with the building authority etc.

everything also clarified with the authorities.

What exactly does the building authority say?
It is definitely the case that the neighbor’s existing building must not be affected. Whether you like it or not. It may be that with the barn a second building with residential use is permitted to you, but with consideration to existing buildings.
You really have to make sure that the roof does not fall off the battens for them.

The barn must also be removed for detached house development on the property

If you were only going to build one house, it wouldn't have to be removed. If you now want to use the property differently, why should the neighbor give up his barn for that?
Then find a building expert and clarify whether your part can be demolished without damaging his part. Otherwise, discuss with him whether you can build him a new replacement building.

I'll pay him for the restoration from my side. The only question is whether he's on board or not. Because one can assume that maybe his barn roof/tiles might also need to be renewed – then he would also have an "added value."

I don't understand how you come up with the idea that the neighbor is on board just because you want to use your property differently. This is not about what you do out of goodwill, but what you have to do. It is absolutely legitimate that he must be able to continue using his barn as before. If changes have to be made to his property because of your demolition, then you are responsible for it, not him. Apparently, from his side, everything could just stay as it has been.

It might be different in the case of an illegal building. It's best to call your building authority and ask there.