LAN and Wi-Fi "devices" per floor?

You don’t understand. I already wrote that you could connect a switch to the socket (with power losses). Double socket is not an option. A modern house already has more connections in the office and living room than you have in total. That should answer your question. Wifi only for mobile devices. Everything else to LAN.

My electrician (...) explained to me that I need this switch in the basement between the patch panel and the router. I didn’t know or know more than that. Is that then "wrong" or "impractical" etc.? I didn’t really want to have more than one access point in the individual rooms.

Yes for the electrical installation, but for network planning this is usually not a good idea! Was there at least a measurement protocol for the installed cables? For me, this would be the only reason to have everything done by the electrician.

Since it sounds like you are not very deeply involved in the topic, I would go for the Fritzbox. Where will the router be located? The area around the router must have good Wi-Fi. The choice of the model depends on this. You also don’t have to place an access point in every room. Less is often more! What you really need you will have to test. If several LAN ports are needed then either a switch with an AVM repeater (but operated as an access point) or you could also use a Fritzbox from the 4000 series and operate it as an IP client.

I don’t find the situation particularly great, but believe me, there are still newly built houses without network cabling where you can only use [Katastrophe].

There was no measurement protocol. The electrician is not exactly proactive, and I lacked (and still lack) the knowledge.
The router will be placed in the basement in the technical room. Good Wi-Fi is not needed there.
The electrician routed the LAN cables into the patch panel and said that as soon as there are 5 LAN cables, I need a switch which, on the one hand, must be connected line by line to the patch panel, i.e. 7 in my case, and on the other hand, the switch must be connected to the router. All in the basement. Is this now correct and sensible? And if yes: is there a recommendation for this switch (brand, model)?
I thought that in the individual rooms we are "basically supplied" with 1 LAN to have a good "basic signal" in the room via LAN cable, thereby achieving sufficiently good Wi-Fi in the room, or even beyond that, and if needed, getting full performance at the end device (laptop) by cable from the wall. And yes, maybe one access point per floor is enough, which I would try, but before trying I wanted to ask which device(s) I could best / first try this with.

What you write is completely correct. The setup is [Router in the basement] --(one cable)-- [Switch in the basement]--(many cables)--[Patch panel in the basement]--(many cables)--[room connection]. "Actually," you could also omit the patch panel; it doesn't do anything. But it allows you to firmly screw in the cables from the rooms and then connect the respective patch panel port to the switch. The switch, in turn, brings the data from the many rooms onto the single cable to the router. Even a simple TP-Link TL-WR940N WiFi router for 20€ does everything you want in the room. The data rate is also completely sufficient. The only reason for "faster" WiFi is possibly simultaneous transmission over multiple WiFi devices (six kids streaming Netflix on their phones). Then it's good to spend a little more, e.g., Linksys EA7500v3 for 50€. All these inexpensive access points / WiFi routers operate with their own power supply, meaning you need a power outlet and the cable lies around. In contrast, PoE supplies power via the LAN cable, so you can save the power outlet. The devices are a bit more expensive, e.g., NETGEAR WAX214 for 100€, and usually DO NOT have an additional LAN port, meaning LAN (from your router/switch/patch panel) goes in, but there is no port for a PC or TV. So suggestion: where multiple devices really need to be connected via cable (e.g., living room), place a router WITHOUT PoE, then you have multiple ports and plenty of power. In the other rooms, place a WiFi access point WITH PoE, so the ugly cable to the power outlet is eliminated.

Router in the basement. Switch in the living room and office (no router).

Router in the basement. Switch (not router) in the living room and office.

The discussion can now be carried on endlessly. The devices that probably make sense here are usually sold as "Wi-Fi routers"...

He has the access in the basement and also planned it that way. And no, a "WLAN-Router" is something different. He only needs one router in the network.