Unifi NanoHD on concrete ceiling - which box to provide?

For example, there is not full reception even in the adjacent room.

That is not surprising at all, especially for 5GHz. That is why it is generally advised to position the APs where they are used the most – for example, not in the hallway if I spend the whole day in the office and want to use it there.

Ok. Then I guess that's how it is. But I am a bit surprised. But overall it works quite well. I am just still looking to set up little things like [Gäste WLan] or something. I can't find anything there. In general, the app is rather poor.

I can't say anything about the app, but the range issue is largely independent of the manufacturer. The only way to really make a difference here is to make changes that are not allowed, such as stronger antennas, more transmission power, etc.

Which app are you referring to, the Android or iPhone APP? Then I'm out, because years ago the app was very poor. It may be better now, but I switched to the controller software. It runs on a RaspPi for me, but it doesn't have to run 24/7 and can also run on a PC for setup. It is important to always work with only one device. The configuration is only stored there. If you switch to another device, you first have to restore the configuration backup, otherwise you have to start all over again. The controller software offers you everything (and much more) that the average user can imagine. Back then, I got familiar with it using IDomiX videos.

The Unifi devices are usually not the fastest in tests, because the design is more about stability and many users. With a wall, almost every device will have a drop in the 5GHz network.

Android app. But the software costs money? Then I guess I'll have to live with it... Although actually everything works. There's no big reason to complain. I just forgot the cable for the terrace... Hence the fear that it might not be enough. Although the access point on the ground floor is not yet fixed in its proper position.

No, the controller software costs nothing. You can download it directly from the Unifi homepage. If you want it to be simple, then put it on a Windows PC. A Raspberry requires Linux knowledge, and if you don't have that, it takes a while until you have everything running on the RaspPi.