Subsequent transfer of plots after purchase - who pays?

You didn’t write anything about the path being necessary...

True. Yes, it is.

In the terraced house, then your fate like about 20% of all detached house owners. That many detached houses are actually terraced houses.

Is that really so? Here in the settlement there are almost only terraced houses. All have gardens either accessible via a service path or with access to the side streets. I don't know a single “trapped” garden.
But okay, not the topic.

Then teach the parents that they have to pay again because they messed up. Or be kind and nice and cover the manageable costs yourself.

The smaller the amount, the easier I can communicate it. But the notary doesn’t disclose any figures.

The smaller the amount, the easier I can justify it. But the notary does not disclose any figures.

You can calculate it yourself. Take an amount of €5,000 and look for a notary fee calculator online.

Well, now from the parents' point of view, you want to have the path (doesn't hurt them to still own property there), so I would somewhat see it that you contribute... but yeah, it just turned out badly.

Well, now from the parents' point of view you want the path (it doesn't hurt them since they still own property there), so I would somewhat see it that you pay for it... but yeah, it just turned out badly.

From the perspective of both parties, the path has already been sold and paid for. Which is legally wrong, but that's the perspective.

One could also say: My parents accidentally delivered only a part to us at full price.

We will settle this civilly among ourselves, after all, there was no intent. They certainly won't come and say: "Well, YOU want something?!"

Why does the question of blame need to be clarified within the family at all? You yourself write that it certainly was not intentional. Share the blame just like the additional costs among yourselves and put the matter down as one of those things that just happen in life.