Is the window installation correct? Is it wind-driven rainproof?

Maybe I also have the wrong perspective ... no idea

As and often say here, "like master, like man" or "what you shout into the forest" you have a certain influence on the quality grade of the Pappenheimers you deal with and how they behave. Therefore, I don't think your wrong glasses have to be to blame if you know positive examples.

What kind of site manager is that, not an architect or civil engineer?

We are building with a local construction company. He used to be a carpenter and roofer, now a site manager for about 10 years.

To me it reads more like the client has saved money in the wrong place. I wouldn’t be surprised if there is no execution planning at all and that the site manager might be a "skilled worker" from perhaps the general contractor.

Sorry, that’s of course the famous crystal ball.
But something like that doesn’t exist if qualified professionals are on site.
Especially since this applies to the entire building and not just one trade where botching is going on.

I haven’t asked yet whether there is any execution planning. We had an appointment yesterday with a roofing expert because the eaves construction does not comply with the technical rules (significant water pockets due to a too-high wedge beam). Two site managers and a roofer assured us that the roof would be watertight for 50 years and that it was produced the same way on all other buildings with low roof pitch (they really build a lot of houses here and have a very good reputation). The result was that the roofer stormed off the construction site in anger and we continued our friendly conversation. I am sure the construction company will present us with a solution that complies with the technical rules.
I brought up the sealing of the floor-to-ceiling windows casually. Oral result: the expert says the weak point is on the side between the aluminum strip and the roller shutter rail. Both site managers: “Nothing will happen there, we always order the aluminum strip from the factory additionally.” You don’t have to seal against pressurized water and a gutter has to go there anyway. Nevertheless, suggestion 1: “We can just remove the aluminum strip again if it bothers, then the water can run down the roller shutter rail.” Suggestion 2: “We’ll just drill a hole in the aluminum strip at the position of the roller shutter rail so the water can drain off.”
What bothers me is that I’m slowly starting to think I’m a pedant. On the one hand, I believe them that they always build like this and never have problems because they are really big here, build many houses, and you can’t find a negative reputation. The site manager is always reachable by phone and kindly answers my questions. On the other hand, I don’t want to pay so much money and end up being the fool, especially regarding the tightness of the house, since all these online stories make you more alert (at least me).

Just to sleep better, I think I will contact a masonry expert whose field also covers sealing. Unfortunately, a window expert is not nearby.

I have not yet asked whether there is an execution plan.

You can recognize it by the detailed drawings.

What is someone supposed to manage construction supervision for, if no execution planning exists? In addition, there are specialist plans such as the airtightness concept,....

But if something like that is not commissioned,...in such cases, the client must look to themselves. The job of the craftsmen is not planning but execution. Then coming with experts,...they would first have to ask for the planning as a basis and which details the craftsmen received. One can only hope that the craftsman raised concerns beforehand and thus does not bear the costs, because they can only be passed on to other clients.

The rails were certainly delivered loose by the manufacturer, as often the roller shutter rails are. The manufacturers know "why",...

if there is no execution planning

... every craftsman does whatever they think is right, and then comes the flood. Then the next trade would also like to do what it thinks is right, but can no longer, because ideally something else is already in the way. So it has to go around, under, or over. That costs at least extra hours and often entails risks with some chasing work. We no longer live in 1980, when underfloor heating in every third screed was the pinnacle of high tech, controlled residential ventilation was not yet invented, and there was only a single lamp outlet per room in the ceiling. A house today is basically a livable fully automatic system and without documentation of the routing of lines, maintenance becomes a serious problem. You can no longer just let the shell construction run as an improvised jam session. This applies even more strictly to smart alecks who, in the hunt for the last penny to save, also assemble a team that hasn’t practiced together.

What is someone supposed to manage construction for if there is no execution planning? On top of that, there are specialist plans like the airtightness concept,...

But if such things are not commissioned,... in such cases the client should look to themselves. The job of the craftsmen is not planning but execution. Then bringing in experts... they would first have to ask for the planning as a basis and which details the craftsman received.
One can only hope that the craftsman raised concerns beforehand and therefore does not bear the costs, as he can only pass these on to other clients.

The rails were certainly delivered loose from the manufacturer, as often is the case with roller shutter rails. The manufacturers know "why",...

For me, it is self-evident that a house is built according to (execution) planning – it is rather sad if such planning does not exist, since the house almost can’t turn out properly then. If the general contractor assures me that everything is fine, I naturally have trust in that first and foremost; otherwise, I would not have chosen the general contractor from the start. But sometimes, I catch myself too often questioning things or informing myself about certain executions. The big question one must generally ask when building is whether to trust the opinion of a craftsman/general contractor who claims to have been doing everything this way for 10 years and has executed all his constructions accordingly or not.
I am definitely sure that execution plans exist, since some craftsmen had such documents with them. Currently, however, I do not want to dig any deeper because the eaves construction is being revised due to water pockets, and everything there has to be redone. Another topic...
The aluminum rails under the floor-to-ceiling windows are requested by the general contractor to be pre-assembled at the factory. They tried several things, and this was the best solution.

..... This applies even more strictly to smart alecks who, in pursuit of the last possible cent to save, assemble an uncoordinated team.

That is of course fatal.