Wiring for AP, choosing the correct network cable

And when it comes to the cable, make sure that each conductor is made entirely of copper. There are also CCA (copper-clad aluminum) cables which are cheaper, but the conductors are much more fragile. CCA is often found in large online stores.

I'm jumping in here, we will probably get fiber optic for our construction project since Telekom is not interested in operating in our small new development area and the regional fiber optic provider is currently very active laying cables here anyway. Is there anything to consider regarding network installations in the house? Specifically cables or similar?

Rather not. The fiber optic cable is "only" laid into the connection room. There you should then let the cables laid in the house converge. In the normal case, your electrician will offer (at least) Cat.6 on their own initiative, so that you will not have a bottleneck at first.

Additionally, "fiber optic" does not always mean "fast." At acquaintances in a town near Luxembourg, everyone has super-duper fiber optic, but the Luxembourg Post barely delivers around 25 MBit there.

Yes, such a thing is supposed to exist. But even if gigabits are not possible there today, the internal wiring should still be future-proof. ;)

but that applies only from at least Cat.7 cables. Better Cat.7a or 8. Neither Cat5(e) nor Cat.6 have met the current standard for what feels like 20 years ;)