Do you need LAN cables in the garage?

With 500€ and "Sinnvoll-Budget" I would definitely save the cable... You will surely be able to invest the money even more sensibly;)

It is a property developer electrician

I will talk to the electrician again to make sure he charges the same price as in the house.

In the house, CAT7 costs 250€

Would you have it installed in the garage for 250€ (if he agrees to that price)?

Is that sensible there?

You have to ask yourself whether [DIR] is worth €250 to you. None of us know your budget / your income / your hobbies / ... That's the difficult part about building a house: decisions, decisions, decisions

Have the shell builder lay a conduit (black corrugated hose) from the utility room through the garage floor slab. This way you are flexible and can later pull through a power cable as well as a LAN cable.

Well, if you are already persistently asking whether it makes sense, then you can hardly imagine yourself whether and how you need a connection there. So it doesn’t seem to make sense to you. Unless you want to upgrade the garage to hang out inside and drink beer among hobby equipment. That is still often done in the Ruhr area, despite a single-family house next to the garage.

Boy, oh boy, 250 per LAN in the house is quite a steep price. Now it's too late, but it would have been better to improve the construction service description instead of later sampling at pharmacist prices. Only corrugated pipe as mentioned above is probably good. But presumably it's about the penetration (airtightness and watertightness, warranty) of the building envelope that the electrician is "afraid" of, or wants to have paid dearly for. However, this may be extremely complex due to a special wall structure and he might be right to charge such prices? But then a big difference between Simplex and Duplex is at least not explainable (how high is it?).