How to decouple border cultivation (next to my house)?

Hindsight is always 20/20. If I had been present during the work on your property, especially under your floor slab, I would have called the police immediately.

It's unbelievable how some people go through life with elbows out.

This is basically already too late now because of the cast-on base plate.

Even a common clean layer should be avoided: otherwise vibration/sound transmission is possible, and ultimately both building structures must be able to move individually. The new building may still settle somewhat during the first winter-summer cycle, which is made more difficult if it is structurally connected to your (no longer settling) existing foundation. Styrodur is the right choice because it is very pressure-resistant, yet flexible, waterproof, and thermally insulating... but it should have been placed between the foundations already, not only at the walls. If nothing is placed between, it will tear off again, fill with dirt, and then you get capillary action, friction, sound transmission, and so on.

After that, the neighbor had his approximately 30-40cm thick floor slab constructed and pour it directly against the concrete of the underpinning (without decoupling). Johann

Hello Johann that is the only mistake I can find. The floor slab should have been decoupled from the underpinning. Styrofoam is well suited for that. But aren’t you somewhat detached from reality in your anger? A 30-40cm thick floor slab? Why would anyone waste so much concrete? Did you document the work, especially the pouring of the floor slab onto your underpinning? That would be a completely amateur mistake that no construction worker should make. Steven