Purchase of a building plot with traffic area

I ask myself the same question, how/whether it works to "take over" only one of the two surfaces from the KV.

I believe the OP should discuss this best with the notary. Perhaps the contract can be designed so that it is valid for each individual partial area even if the city exercises its right of first refusal. I am more interested in whether the seller can still withdraw from the purchase contract, which of course would not be in the interest of the OP. Actually, I would recommend not doing business with such obstinate individuals, but I know how difficult it is to get affordable buildable land without complications...

Okay, so the municipality necessarily finds out about it and can still exercise the option, but only by buying into the entire purchase. They would hardly want to do that because they are not interested in the building plot area and cannot afford to acquire it in order to separate the traffic area from it.

I also wonder how/whether it works to "grab" just one of the two areas from the land register.

That will not work. The OP should clarify this for us – I suspect I have misunderstood something:

The plot itself has a size of 543 sqm and additionally you acquire a 108 sqm traffic area.

I had interpreted this to mean a 651 sqm plot with a 108 sqm traffic area, but especially the remark

She wants to grant us a right of use for it.

also allows the interpretation that the mentioned plot has a total of 543 sqm for building and there is a 108 sqm share in a traffic area that runs across several plots, which the seller holds separately and only wants to grant a right of use (GFL) over it. So this is now the question: are the mentioned 108 sqm a) a GFL area on the desired plot that is not marked as a parcel; or the seller’s share in a private shared road, which b) is not marked as an independent parcel or c) represents an independent parcel?
And: can the OP waive this use because his future plot also borders the public road and can be developed and accessed without including this traffic area, so that he would lose no more than a GFL right acquired but not strictly needed?
Without corresponding clarification, further speculation would probably be the proverbial quarrel about the Emperor’s beard.

Or is it a partial area in the sense of "sharing," meaning all adjoining property owners hold an ideal share in this traffic route? But yes, so far speculation, we will probably have to wait for clarity..

I would have interpreted the original description from the OP as selling a building plot plus a share in a pathway parcel. (That was also the case with us back then.) In this respect, the city could only exercise its right of first refusal for this share. However, I would find it much more interesting to know why the city might want to acquire this part, but of course, this cannot be said without further details. (My contacts at the local town hall say that purchases are only made with a concrete reason, as it also costs money, which the municipality regularly does not have.)

The OP apparently enjoys our guessing game