Rainwater drainage on the property is unclear for the building permit

I do not mean a specific institute, as I have not researched specifically for you. Research and development is carried out on almost every topic. Special solutions can be found in this environment. Often things have to be tested in pilot projects / pilot plants. If I were to research, I would start geographically in the Netherlands, northern Germany, and around the brown coal open-pit mining area.

You are building with a developer? Then you only gain ownership after acceptance and final payment...
Therefore, the whole issue is rather the developer's problem.

Since there are existing houses, the groundwater situation cannot be that bad.
Hopefully, you have a contract with completion deadlines. The groundwater situation is known; the developer cannot claim force majeure here. He should have known that foundation and drainage could be more complex.
Talk to the others affected and then put pressure on the developer.

Unfortunately, the property was purchased privately. Until the building permit is granted, there are unfortunately only deadlines that will increase the cost of house construction. Therefore, we want to proactively address and advance the issue.

Today it emerged that the following proposal is being developed: cistern, grey water usage, and overflow into the activated soil zone or an infiltration basin in the rear garden area.

The infiltration basin in particular is causing us headaches. Can it be used for playing? Is only grass allowed there? How else can it be designed?

Here is our property:

Greywater use is "expensive". Double piping, filtration, switching with separation, etc. If the property is privately purchased, it is not a developer.

How could the infiltration swale possibly be optimized/beautified/made usable?

You can build a wooden terrace on it, so the idea of having the swale close to the house is also nice: implementing a rock garden/pond in the swale.