LAN cabling in single-family house (prefabricated house)

If you want two LAN ports, do you also have to run two Cat 7 cables? Is that correct, just out of curiosity.

Yes, exactly.
For me, 1 LAN connection costs €68.75. I have about 16.
Additionally, 2x 8-port patch panel: €104.38.
Then a flat connection fee: €280.

But everything is included in that.
With tax and discount, I am then at €1678 for the whole house.

Your €300 sounds very cheap then.

Depends on what he still wants for the installation etc. Sounds like a cost trap. For us, a double socket cost 95 euros net, with wiring "all-in".

If you want two LAN connections, do you then have to run two Cat 7 cables? Is that correct, just out of interest.

For Ethernet (LAN) with 100 MBit you only need 4 wires, in a LAN cable there are 8 wires, so you could connect 2 ports, however this is usually only done in existing installations and if there is no other option, but not in new builds, as it limits the usability of the port, for example PoE is not possible and instead of 1000 Mbit you only get 100 MBit throughput.

Cat7 has 8 cores, to fully utilize it on 1 it is better to have one cable per socket, with two sockets two cables, right?

That is then a duplex cable, basically two in one, each with 8 wires. So you don't really have to pull 2 separate cables.