Abnormal parking space regulation - legal action or ignore?

If I didn’t mismeasure from the plan drawing, the garage is planned with an interior dimension of seven and a quarter meters.

Very good! According to §4 GaStellV, the garage is already sufficient for three (2.40m + 2.30m + 2.40m = 7.10m required clear dimension).
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A nitpicker might now still complain about the too narrow driving aisle for the yellow car, but I spared myself rotating this parking space by 30° now – the planner should also have something to do for his money.

Isn’t there also an exceeding of the floor area ratio?

No. But I’ll only believe that the two-story construction will be approved once the approval is granted.

Whether, if checked, I could then be forced to actually build the parking spaces

Yes, certainly.

Buyout

… is usually the last resort in case of unreasonableness, which certainly cannot be said of this plot.

The question is exactly which "obligation" one then enters into with it

Well, the parking spaces then become part of the building permit. If you don’t build them, you violate the building permit and there will be an administrative procedure, with fee notice, hearing, deadline setting, fine, coercive fine, …, prohibition of use, forced eviction – ok, exaggeration makes it clearer

… and whether and how one might still get out of it in case of doubt.

You can still build them within the deadline where they were approved or submit a new building application.

A great idea! With 3 parking spaces in the garage, it doesn't look so bad anymore. Many thanks for the valuable tips and advice!