Network planning for a newly built semi-detached house - sensible or possibly overkill?!

You will most likely not have the same spacing between the ports on the keystone panel as on the router, so it doesn’t really matter which panel you take. The cables will not run perfectly parallel from panel to switch. Possibly a 24-port panel would be sufficient and the rest of the module openings can be closed with blanking plates.

With the 7590AX it of course depends on the price you paid. Because of a 30 euro price difference, I wouldn’t bother sending things back and forth again and would keep the Fritzbox. Who knows, maybe a feature will still come via update that the smaller ones won’t get.

We do not use landline telephony.
The long update support speaks in favor of the FB – I actually don’t see much added value right now. Too bad, I thought you could convince me not to send that good thing back :)
So stay with the 2-3 Ubiquity access points and don’t switch to AVM. Then turn off the WLAN of the Fritzbox.
Do you think it makes sense to also replace the switch once more with a "managed" switch? We don’t use MagentaTV so far.

Since I have a 16-port switch (I specifically chose one that has all ports next to each other so I can easily wire symmetrically from top to bottom to the patch panel), I am currently still looking for a 16-port keystone patch panel.
For a 16-port one, I indeed only find the "faceplate," without the structure behind it:

I would prefer something like this: , behind which I can still secure the installation cables. What do you think?

For the requirements, of course, any current FB that supports Supervectoring up to 250 Mbps will do. You only need modem, DHCP, and DNS.
No landline means you only use mobile networks for calls? Then that of course also falls away from the requirements.
Just keep in mind that in modern houses, reception can be very poor and WLAN-CALL does not always work perfectly either.

Regarding the switch, if you want to keep the possibility of VLANs open, then you need to use a different caliber anyway. Since the Fritzbox does not have the necessary routing for VLANs, you would have to put a second router behind it that handles this or use a DHCP-capable switch.
If none of this matters (nor in the future) and Magenta TV will never be a topic, I see no reason to go for a managed switch.
Because just because a switch is called that by the manufacturer does not mean it actually brings added value. There’s a lot of marketing involved. To be on the safe side—regarding what manageable should actually bring—it must be a Layer 3 switch that supports at least static routes and then you need a different router than the FB or directly a switch with its own DHCP that could run right at the FB and thus take over all routing completely.

the house + garden should be supplied with Wi-Fi

No one has written anything about this yet, but if your garden is larger than 20 m², you should also consider an outdoor access point, because with today's 5 GHz (and 6 GHz will also be starting soon) the range ends shortly behind the patio door. (With 6 GHz, the range will be even more reduced.)

Since the transmission power is limited in Germany, the Unifis are similar in power to other decent products.

It is also strongly discouraged to activate the USA as the location in the configuration. This would lead to a non-compliant increase in transmission power with some Ubiquiti devices.

Apart from that, you also lose some usable frequencies as a result.

It is also strongly discouraged to activate the USA as the location in the configuration. This would lead to a non-compliant increase in transmission power on some Ubiquiti devices.

Is this a hidden tip to tune your access point?