The city wants to dissolve the street and offers the area for sale

So it's about the street above the house

No, that is actually only useful as a cadastral map with parcel numbers, etc., a picture would practically say nothing "usable" to outsiders even if it were more recognizable.

my back exit (which I mainly need for my bike) would then lead directly into their garden (i.e. I could no longer use it),

What is the status of the expropriation procedure (the area would have to be decommissioned, including hearings/rights of objection of those affected),?

If you plan to sell the house, it would still be worth considering, as additional parking space at the house as well as a small green area (even if it is just a raised bed) would likely increase the value significantly. You might get the investment back twice over!

Yes, it definitely makes sense to increase the living value, when I bought the house back then and there was no parking space, that was more of a negative point, but the house was very cheap 7 years ago. I'll just see what they want for the whole thing and what the neighbor says....

If you want to buy, clarify whether the street will actually be vacated. You don’t want to have to keep it open for third parties and traffic-safe. Personally, I would prefer if the current surface were disposed of at the city’s expense and I could maybe create something new myself with grass pavers. Otherwise, you always have to hope that the surface NEVER has to be removed by you, as depending on the age and contamination, the disposal can be quite costly.

If you want to buy, clarify whether the road is really being closed. You don’t want to have to keep it open for third parties and traffic-safe.

Yes, I think that is not quite clear here yet. The original poster wants to receive the area as their property for free disposal, not as their share of a private road that is still burdened with third-party rights of way and so on.

The usual procedure, which does not happen automatically, is as follows: the municipality as the maintenance authority – or an interested adjacent property owner who wants the area – asks whether the public still (or at all) needs this road. Then it is announced for abandonment (caution: possibly only publicly, instead of notifying every affected party! – I’m not exactly sure about that). After the affected parties have given their opinion, the municipal council must formally decide on the closure of the area.

The municipality must of course clarify whether the parcels of land would be purchased from them: it cannot keep any if it can no longer access them ;-)

And unlike the construction of the road, where the necessary areas can be expropriated, no one can be forced here to want to have the parcels.

The typical initiative therefore comes from one of the neighbors who wants the area – usually preferably in its entirety*. Among other reasons, that’s why I say, bring a cadastral map. So far we don’t even know whether "your section" would be its own parcel. It would be highly unusual to parcel the road for that purpose.

*) also with the consequence of having the area alone without offering the neighbors rights of way.