House purchase: Terrace missing in the land register

...and the defect is obvious to anyone who is not blind. Therefore, there is nothing to get from the previous owner.

So keep your mouth shut and live happily in it (and invite the neighbors over for a barbecue sometime).

And the worst thing that can happen is that you have to dismantle it sometime in the future. In 2, 5, or 25 years. With luck, never. Definitely better than taking action now and then having to dismantle it for sure this year.

I thought that such changes can be recorded in the land register to ensure legal certainty (after agreement with the neighbor).

It is not the terrace that is recorded, but the necessary transfer of the setback areas to the neighbor for such a structure. However, that would then be recorded on their property and not on yours. The problem is that the neighbor is then not allowed to build anything in the double setback area and is usually unwilling to legalize such a thing.

Get along well with the neighbors, there might be a tolerance granted at some point because it has been like this for too long if someone complains. But keep in mind that you have already received something from the neighbors in case they come knocking for any reason.