Is a TAE socket no longer needed?

Thank you very much for the tip! Unfortunately, we can't get the LAN sockets up to the ceiling anymore, but at least there is a double socket next to the power outlets in every room. In the living room, there are even two double sockets: one at the spot for the TV, and a second one on the wall facing the garden.

In the basement, we're doing it like this now: network cabinet next to the fuse box, with the router in there as well, and then, as you recommended, one access point per floor.

From the manufacturer you recommended, these APs would make sense for us (wall installation, no special requirements), right?

U6 In-Wall approx. €200
U7 Pro Wall approx. €215

I haven't understood yet the difference to the cheaper Ubiquiti UniFi U6+ (€100) and the (round) Ubiquiti U7 Pro (€180), but I will research it.

U6 In-Wall approx. 200 €
U7 Pro Wall approx. 215 €

I have not yet understood the difference to the cheaper Ubiquiti UniFi U6+ (100 €) and the (round) Ubiquiti U7 Pro (180 €), but I will research it.

The difference mostly lies in performance. The U7 Pro, for example, already supports WiFi 7. The Pro variants are for "large offices." The Plus variants are for small to medium offices, and the U7 Pro Wall is "tailored for home builders with seamless installation options." I haven’t used that one myself yet, since we mounted ours on the ceiling, but they look solid. The "Paintable Flush Mount" also looks pretty cool if you want to take it a bit further. And if you need newer WiFi standards in 5-10 years, it’s completely sufficient to just replace the APs.

The APs can be set up with the corresponding app, but if you ever dive into home automation, they can be better managed with a server that offers even more functions. That could be, for example, the Dream Router from them. With that, you would have everything in one and wouldn’t even need a Fritzbox anymore, but you would need a modem. The Draytek Vigors for DSL are apparently common for that.