Non-compliance with the development plan by the neighbor

1. There is no backstory. 2. He knows exactly that it bothers me and nothing is happening behind the scenes. 3. As far as I know, one might talk to the neighbor before building something on the border... everyone has a mouth. Yes, he wants to sit by the water... but this does not justify the construction... or one could have also stayed 3..4m away from the border. Besides, I have already planted a hedge... but unfortunately it is only 1m high so far. I probably have no choice but to wait for the fence and my growing hedge. And I will just build whatever I want there... but I will discuss it with my neighbor to do it legally... Also, a terrace is something different from a small garden shed... in my opinion. That’s how he sold it at the beginning.

That's how he had sold it at the beginning.

So he did announce it in advance after all?

He started working there and I asked what it was supposed to be.

A small hut.....I didn’t care.

25 sqm terrace.....never mentioned....I would have cared.

Since he has already fully used the boundary building line with his garage, he would have actually needed my permission beforehand for a hut too.

It simply annoys me that people apparently no longer manage to be talked to and to show some consideration for their fellow human beings.

I did not talk about whispering but one can speak and let 3 gardens participate or speak quietly. These are not hearing-impaired people but young people.

I think consideration in daily coexistence is not wrong. However, I do not solve problems that way if I myself am inconsiderate.

My "direct" neighbors, we are separated by a 5-meter-wide path, have their screaming grandchildren there during the day and from 11 p.m. a group of adults comes out of the house and then they start grilling, smoking shisha, and talking loudly. Audible even through closed windows. Wonderful in summer. Earplugs only help to a limited extent. Moving away is currently not possible and not an option. Being loud myself is not an option, because unlike them I have to work the next day.
So I call for quiet. Works to some extent. Works better if I explain it to them after ringing for a long time at 5 a.m. The next step is the police.
Well, why did I move there? Before they moved in it was a great quiet residential area.

The neighbors 3 gardens further also work, so at least during the week it is quiet after 10 p.m.

To be honest, I wouldn't think of speaking extra quietly on my terrace... unless I say something so private that no neighbor should hear it. In return, of course, I don't expect others to speak extra quietly either. It is their decision what they want to share "with the whole world" and what not. It is of course different if it happens at night/late in the evening/early in the morning. Then I naturally make sure not to be too loud and expect the same from others... except from small children who don't understand it yet

Hmm... the real problem here is actually not the terrace, but that it is being used.
As already noted, you can hardly forbid the neighbor from staying on this piece of his property.
Whether there is a terrace or grass underneath doesn't change your problem.
So I think first of all, take a step back and observe whether the terrace is even being used.
If he sips coffee there twice a year, I wouldn't start a quarrel over it.
If he spends half the day there every day, well, then you could consider doing something about it.
If you really want to build a hut there anyway, just go ahead and do it; that will solve all problems.