Excavation beside foundation/underpinning

According to the description, the garage should have already settled.

... and indeed to a degree visible to the naked eye.

Thank you very much for all the really helpful answers!

Update:

[*]We called the building authority this morning and explained the case. Around midday, someone came directly and shut down the construction site.
[*]The excavation pit had to be refilled and compacted up to about the bottom edge of the foundations.
[*]Now a structural engineer has to calculate everything and create a plan for how it can be properly implemented.

Regarding the questions about the foundations: The garage consists of several precast concrete parts that rest on strip foundations. The strip foundations run parallel to the street, each perpendicular to the edge of the excavation pit. This probably prevented worse damage.

We have documented the previously completely crack-free condition of the garage with numerous photos. We will also mark with the cross laser. Can we still do something to protect ourselves in case the soil under the foundations has loosened and settlement cracks develop in one or two years?

Pools may apparently be built within the setback areas in Hesse as long as they do not protrude more than 1 m above ground level, as someone here had already posted.

Pools are apparently allowed to be built within setback areas in Hesse as long as they do not protrude more than 1 m, as someone already posted here.

Specifically - I don't understand what is supposed to be nice about a pool that is directly attached to the neighbor's garage wall...

We called the building authority this morning and reported the case. Around noon, someone was already there and shut down the construction site.

Then the authority also sees this as more than critical. So let it be. Thumbs up

Great success! What interests me: what did the neighbors say about the action? Did they ever say what they are planning? Size of the pool, etc.?

Specifically - I don’t understand what is supposed to be nice about a pool that is directly glued to the neighbor’s garage wall...

Maybe the optimal wind protection? It may also be that the garage wall is a visually nice surface that provides a beautiful background, especially if you then plant grasses on the left and right. I would never exclude a nice appearance when reading something about a house or garage wall. I prefer to look at a well-maintained quiet surface rather than at patchy greenery from the neighbor, behind which there is the mega trampoline.