Which smart home system is suitable for our new building?

I used to always call TP-Link "junk." Nowadays, you can't really say that across the board anymore. But TP-Link is certainly not generally better than AVM, rather the opposite. If I were you, I'd really go for the AVM 6000 series; you'll be quite happy with it. Maybe you can still find a high cabinet where it can be hidden. There are also 3D-printed mounts for that (e.g., mounted behind a curtain?). If you don't need POE, you'll be happy with the really good AVM Mesh; you don't need centrally managed WiFi like with Unifi.

I can't recommend a TP-Link router; the new AVM 7590AX fits very well with the aforementioned repeaters (which should please be configured as LAN bridges). Often, the rule is simply: do what the majority does because it works.

Oh I had rated TP-Link Omada as close to Unifi or almost on Unifi level since the Omada system is also intended for professional use. On a test site, the Omada system was evaluated as very similar to Unifi. Yes, there is probably a taller cabinet where I can connect the access point and supply it with LAN. Then I wanted to ask something I still haven't understood: What can a Unifi system do better than an AVM system? What can you do more and better with Unifi than with AVM? Was it just the advantage that Unifi can be powered by POE? (making ceiling and high wall mounting possible?)

central management of all connected Unifi components ... That (and POE) simply doesn't work with AVM (or only very limited with Mesh)

The developer has thrown a wrench in our plans. The developer does not allow the electrician to prepare ceiling access points due to the statics.

Sorry, but I have never heard such nonsense.
Are you also not allowed to install lamps on the ceiling because of the statics?

We find wall access points visually very unattractive and would rather have them installed hidden (even if the performance gets worse because of it, I don’t need Gbit over Wi-Fi).
Because of the worse position, I would then want to use good APs with the new WiFi 6 standard to compensate for the poor position.

That is also nonsense, unfortunately. WiFi 6 and good APs cannot compensate for bad positions.

Radio waves work similarly to light. So where light does not reach, usually no Wi-Fi reaches either.
That is why lamps are installed on the ceiling and not behind the TV.

Well, Philips Ambilight... But you are right after all...

What does central management mean? What all do you have to manage in a single-family house?

Can you maybe list a few examples so I can see if I might need any of them eventually?

Yes, I know it's nonsense with the statics, but unfortunately I can't do anything if the developer doesn't want it that way, so I have to live with the alternative. But for a bit of surfing, the access point in the cabinet should be enough (I hope).