Adjacent neighboring garage (existing building) with a height of 3.6m

Why should the garage trigger a setback area?

The problem is probably rather that an architect/authorized draftsman who knows about a theoretical distance requirement would deliberately violate the state building code. The question remains how this "offense" is assessed and whether anyone would go along with it.

I do not know the state building code. Why should the garage trigger a distance area? Since the OP does not want to build onto the garage anyway, in my opinion that does not matter.

Yes, it is too high. But it was built without permission or similar. There is also no registered building encumbrance. May it still trigger a distance area then?

Preliminary building inquiries and especially applications for formal building permits reliably avoid the uncertainties and risks of exemption procedures.

Even a boundary-privileged building triggers setback areas depending on its average wall height. And if it "wants" to do so, it requires the acceptance of these setback areas, provided it cannot settle them on this side.

I would be cautious with claims of legal violations; so far, I have not been convinced that the garage would actually be too high with reference to the relevant original plot. I consider it possible both that the garage exceeds the procedural freedom limit without intent and that the OP mistakenly accuses it of being too tall.
If it is a fact that it has too much wall height, this triggers a setback area (for example, 3.5 x 0.4 = 1.4 meters), which would probably have to be "rounded up" to the minimum boundary distance of 3.0 (in BW: 2.5) meters. If no acceptance exists for this, it can probably be remedied by catching up afterwards – but not ex officio against the will of the OP.

So again: #1: apparent excess height and legal excess height are not the same; #2: neighbors can form a “common fund” (= acceptance of setback areas), but only by mutual agreement; #3: violations do not hold the neighbors liable by association.
I won’t say this a fourth time – over & out!

State building code: "The specified ground surface is the ground surface set in a development plan or determined in the building permit or partial building permit; otherwise, the height of the natural ground surface is considered fixed."
According to the development plan, the nearest street centerline applies.

"Violations do not hold neighbors collectively responsible" -> You mean that I must not suffer any disadvantages due to a garage that is "possibly" built too high?

I will not say it a fourth time

Preliminary building enquiries and especially applications for formal building permits reliably avoid the uncertainties and risks of exemption procedures.

#3: Violations do not hold the neighbors accountable by association.

Why would it become more expensive in my case? The building authority would have to clarify the matter with the neighbor.

I would only have the annoyance of the time delay, right?

What exactly do you mean by penalty? Penalty for whom?