Crane swing area in a very densely built-up residential area

Uff, how I could not care less about such people. He surely saw the crane, and just like you googled, and then saw "oh! ha! they should have asked me!

Even just the politeness should have prompted him to ask him beforehand.

Just basic courtesy should have made him ask him beforehand.

A thousand things went through our minds. Just like with everything in life, if you do 100 things right, no one notices. Do one wrong, you immediately get reprimanded.

We are polite, we simply didn't think of it. Otherwise, we wouldn't have let neighbors park their cars on our property, store things destined for the dump on our premises temporarily, etc.

We try to have the conversation, that's all we can do. It absolutely was not intentional on our part.

Just the politeness alone should have prompted him to ask him beforehand.

But you have to know all that first. I don't believe that the OP had any malicious or rude intention there.

I lifted the neighbor's prefabricated pool into the garden with our tower crane and lowered myself into the parents' inspection shaft to retrieve something from the last flood period. Just ask him if he doesn't need the crane's capabilities for the time it is standing there? Such a slewing radius opens up many possibilities. Get a passenger basket and clean/paint the facade, clean the gutters, replace the satellite dish, etc. When such an opportunity presents itself, a thousand useful things come to mind, but not to intervene against it. Stay positive and initiate the conversation (as you plan to) and find a solution.

Of course, the crane stands wind-free outside of working hours, but then without load, and controlled during operation (not by the wind).

We did not say that the crane is responsible for that. Only that the street is closed.

It already reads to me quite clearly like "we cleverly do not come up with the reason ourselves first," which makes me understand if the neighbor is annoyed about it (without having to be a grumpy person because of it).
That a tower crane has a slewing range (possibly also extending over the airspace of private and public land) must be clear to everyone – if necessary with the consequence of having to consider other lifting equipment, and in any case with the one of having to ask other airspace holders for permission (as said, I did not exclude that some regional law sees this differently). I stick to my impression that the OP approached the matter very naively, and renew my question about what the SiGeKo says about it.

Presumably, we will have to live with the consequences if the neighbor exercises his right. Such a close-knit community of residents lives, after all, by give and take. And quite simply, in the past, we have probably seen too much through rose-colored glasses and have not restricted anyone, even when it was at our expense. We simply did not think about whether we were naive in our approach; I dare to doubt it; but I accept your opinion.