Buy a house when the floor area ratio is exceeded?

I would take the house as well. Maybe something can be done about the price. However, you run the risk that your seller will tell someone who later uses it against you if you have a dispute.

Current situation with an acquaintance after 25 years of neighborhood. The neighbor has a new boyfriend and 1-2 things have happened. Since then, there have been accusations about everything (it doesn’t cost anything, as I have now learned). Recently, they had to dig up the foundations to remeasure the boundary. It was 20 cm in the end and now has to be adjusted.

In our development area, there is probably something on every plot that does not conform to the development plan and was probably not approved either. If someone now had to dismantle a terrace due to exceeding the floor space index, then the other neighbor would have to tear out their tree which is not in the planting plan, the other shorten the too-wide driveway, and the other neighbor would have to remove the 20cm too high embankment. Etc. Etc....

I find this important.
If someone wants to harm you, they will find a reason. If the terrace has already existed for 10 years, it will remain there without causing any disturbance. Even in M-V, the inspection authorities, due to limited staff, are not keen on pursuing an exceeded floor space index as long as no one complains.
We are currently building in an existing development plan area. There, not one has permeable paving with 25% joint width or the prescribed number of fruit trees.

If the price is right, go for it.

Simple risk assessment. Worst case is not 5000€. Best case is that nothing happens. Risk in relation to buying a great house is negligible. I wouldn’t worry about it. Absolutely not after weighing it and forgetting about the issue for now.

nothing happens.... when the terrace is 12 years old....

how many people build and then expand or something else

who runs to the building authority for every little thing. I hardly have any lawn left either, never gave it a thought except for outbuildings

Comparison would then probably be "not buying a house because of the terrace" and "catching Covid-19".....

No. Just take what is offered and correctly assess the risk ;)