Build a terraced end house with an additional unit (GÜ) on your own

If you take 3 Ubiquiti AC Lite, you're at around ~240€ and have a clean solution, that's probably the best way.

You’re probably right about that. However, there are an additional 120-150 € per LAN socket as well as the not very nice appearance. Therefore, I wanted to avoid it. Maybe I could hide the ones for the attic in the loft.

I would also always choose star topology for wireless, not least because of signal propagation delays. One access point on the living room floor and one access point on the children's room floor should be sufficient; in the bedroom, you can also stream Netflix via LAN.

Phew, those are expensive cans. The APs don't necessarily have to hang on the ceiling in the hallway. If the look bothers you, just put the one on the ground floor into the TV lowboard or something, the attic is also fine in the pitched roof, they won't be installing a concrete ceiling there.

You are probably right about that. However, there is an additional cost of €120-150 per LAN socket

How about - 1x LAN in the living room for FritzBox - 1x LAN in the hallway on the upper floor for the access point and - one empty conduit each in the basement and in the attic For the latter, depending on the need(!), a cable for the access point will be added.

There is no basement. Empty conduit would of course be possible. LAN connections will be added anyway, this was only about additional connections, e.g. in the hallway for an access point. I would not start using the Fritzbox WLAN just to save myself the access point. If multiple APs are necessary, they should also harmonize, i.e. for example, all from Ubiquiti. The modem/router does not have to stand around in the living room but goes into the HAR or wherever it does not bother.

I would place the router near the patch panel. It will probably be in the utility room in the attic - more details will be clarified tomorrow.

You can also watch Netflix over LAN in the bedroom.

Unfortunately, iPhones no longer have a direct network connection, so I also have to take the "detour" via Wi-Fi in the bedroom.