Which smart home system is suitable for our new building?

Yes, we are talking about a 150 sqm semi-detached house on 3 floors + basement

I also think that 1 access point per floor will be sufficient even if it is not installed optimally

I unfortunately have to ask again what a POE access point system (e.g. unifi) can do better than e.g. AVM
What is the benefit of central management?
What functions does unifi have that AVM does not?
If I know which functions unifi has, I can better decide whether I need it or not

I have not found a comparison between unifi and AVM

Regarding Smart Home, I will first wait for the next conversation with the electrician before looking further into it

Poe does not need a power outlet.
Managed can handle, for example, vlans.

I think you can live well with AVM too. I mainly chose Unifi because of POE, as I wanted the access point on the ceiling. For me, an access point belongs either on the ceiling or high on the wall to avoid being obstructed by any furniture or other devices.

Unifi offers more configuration options than AVM, but very few people need these. Most of the people I know are already overwhelmed with AVM during setup and hopelessly lost with Unifi. There is also the option to set up Unifi via a smartphone app, but I uninstalled it immediately after the first test. For me, the Unifi Controller runs 24/7 on a Raspberry on which Pihole is also running. However, you can also use the controller on a local computer and only start it when you want to make changes. It is important that you cannot simply switch to another computer. You must always first create a backup of the settings and then restore it on the other computer.

And I have nearly my 250 Mbps everywhere in the Wi-Fi...

This will be the speed of your internet connection. But there are also scenarios where more in the local network is great, especially if the laptop is only connected via Wi-Fi.

This will be the speed of your internet connection. However, there are also scenarios where more in the local network is great, especially if the laptop is only connected via Wi-Fi.

It would also be useful to know the OP's requirements again. For example, is a network storage being operated? Is anything streamed over it?

We will get a 500mbit fiber optic connection

Setting up a Fritzbox or for example Vodafone standard router is not a problem
Also opening certain ports is not a problem (I have done that so far)

Can someone tell me how I can secure my network or individual devices, for example for IPTV (do you use VLAN for that)