I can place a garage directly on the property boundary.
That is true. Your first statement
Garages do not necessarily require building boundaries
does not say anything, therefore my question what you meant by that.
A house even if the building boundary allows it
But the house of the original poster is not located exactly on the boundary, but at a distance that is smaller than the minimum distance required by state law (which would still have to be proven). I have never seen such a determination.
and one should know what a building boundary is.
I know that and precisely for that reason I do not understand what you mean with
building boundaries may also be less than 3 meters.
I see a copy of an official site plan - isn’t that an indication that everything is legal?
No. A building can be recorded in the cadastre in different ways. This ranges from qualified building surveying through field comparison to aerial photo evaluation. Therefore, the true boundary distance cannot be extracted from the cadastral map without knowledge of the coordinate accuracy. And even if an undershoot of the minimum distance is determined during a building survey, usually no notification is sent to the building authority.
I do not read anything about an illegal building.
But the original poster asks the question
Or could the neighbor say I have to tear down my garage now?
This question would not make sense if he did not fear that the previous owner had done something illegal on the property.
So everything should be fine, I think.
I think so too. If the new owner has something to complain about or you plan changes to your house, you can open a new thread.