Cost coverage for fencing that is not desired

Exciting, keep us updated.

So after a few days it has now turned out that the fence is actually already commissioned and the landscape gardener is just starting to install it. It will be a RAL 7016 wire mesh panel to match his windows (not ours, by the way). The entire property around is commissioned to be fenced. I told the landscape gardener to please also install the fence on the neighbor's property, as that is not my commission.

What does that tell us now? Interest in a joint solution? Unfortunately not. Let the new neighbors pay directly for their own fence and wish? Gladly! I'll just let it run now. Let's see when he approaches me next, and then I will unfortunately have to tell him that I will not participate in his desired fence without ever having discussed the execution. At most 1/2 chain link fence. Maybe the topic is settled with that and he pays for it completely alone. We'll see.

I'll put it this way. A deliberate color matching to existing window colors would seem rather unusual to me, also because the standard colors are probably limited to 2-3; I personally wouldn't have a problem with that alone.
I would also not accept the described approach nor participate in it. According to my own ideas, I would contribute to the shared border with (for you, sensible and nice) planting and tell him so, neither mockingly nor angrily.
Basically, it has one advantage: The fence belongs to him and the plants belong to you, and everyone is responsible for their own stuff—that's how I would explain it to him.
Getting into deeper discussions with him probably won't achieve anything, but over time the whole thing can lead to a sufficiently tolerable coexistence if one doesn't open a conflict now but instead calmly and factually sticks to their decision, as he does as well. Eventually, the anger or lack of understanding will at least fade, and you live alongside each other.
We also had a few annoying experiences, nothing serious but things that really made you shake your head. Such incursions ended when the buildings and surroundings were finished.
It's strange indeed. I wouldn’t pay anything because it’s on his side and belongs to him alone, so why should I? I would have wanted it differently, he did it his way, so the consequence is that he pays for it alone. If you give him anything, it won't improve his mood anyway, so that's clearly settled now.

Exactly, nothing can be added to that.

.... You don’t have to leave space for cutting behind the hedge; the neighbor is allowed to cut anything that grows over to their side.

But that is then the next point of dispute. When we still had our old opaque wooden fence, ivy and shoots from various plants regularly grew over to the neighbors’ side across a width of about 2 meters. I cut them back regularly, but sometimes simply didn’t notice that they had forced their way through the fence again. On the other side there was an old, broken (according to the neighbors) piece of picket fence. They then very kindly asked us to please cut back our ivy so that their fence wouldn’t get damaged any further. That was obvious to us and the matter was settled.

A short time later we wondered why small amounts of shrub cuttings were regularly lying exactly at that spot. Sometimes a few leaves, other times single shoots. Eventually we accidentally saw that the neighbor woman was cutting the shoots from our plants on their side and throwing them back over repeatedly. Once I caught her in the act and confronted her, but got only a few snappy replies. Since I already knew at that time that they were moving out, I didn’t want to have any more discussions. Later we found out that they had done the same with the other neighbors....

Some people are just like that. Before I let a neighborhood dispute escalate over this, I simply plant my plants a little farther away from the fence and that’s that.

The fence from the neighbors was about 50cm away from ours, by the way. So it wasn’t the case that individual shoots of the plants could cause direct damage. They were simply concerned about the principle.

It is commissioned to fence the entire property all around. I told the landscape gardener that he should also place the fence on the neighbors' property, as it is not my commission.

Exactly like that. But then also make sure that it is really done that way.