Problems with the light shaft, unfortunately water in the basement

A submersible pump that reacts to a maximum height is a good idea - if it is really due to the overflowing cistern.

da ist halt bei der Entwässerungsplanung geschlampt worden.

When I think of the heavy rain events of the last few days, it is quite possible that even a well-planned system can sometimes be overwhelmed.

How is one supposed to imagine that? Does the water rise in the light well and then push in over the window frame, right?

There was simply negligence in the drainage planning. The effort to "straighten it out" afterwards is of course higher. But do it right from the start as already described above. Drainage under the light well, connected to the cistern (so only indirectly to the sewage system) – done. How do you want to supply and monitor the submersible pump with electricity?

We have just laid the driveway, but not yet grouted. Therefore, you could remove individual stones and run a cable duct to the light well.
With a float switch, the pump would turn on as soon as the water rises too high.
Alternatively, just close the window and that’s that... Unfortunately, this has happened for the second time within 2 years and the developer is obstructive...

How should one imagine that? Does the water rise in the light well and then push in over the window frame or what?

Yes, correct. Apparently, there is some kind of river underneath that the water finds and follows. In my opinion, along the house wall under the house insulation :-/

Thank you very much for the answer.
Would I have to rip up the driveway again for that? A drain to the sewer line is apparently not planned by the municipality. I already asked during the house construction and it was rejected.

? Municipality?

The water from the roof flows into a cistern in front of the house and into the sewer.

Aha! The municipality is not responsible for your property - either they or a cistern on the property is needed!
A submersible pump can also work. We had one in the basement of the old house...
Maybe one should simply install another cistern and connect both together?

Does the water rise in the light well and then press in over the window frame, right?

Basement windows are not submarine windows, so they are not sealed against rising water in the basement light well.
We only had peace from water in the basement light well of the old house when we had a cover pane over it and a vertical drainage pipe with a diameter of 40 cm at the house down to the base plate, and a submersible pump to the cistern with overflow into the sewer. All downspouts led into the cistern.
The house had a white tank and in wet years layers of water up to 0.5 m deep under the lawn, just clay soil.