ᐅ Is it necessary to have LAN cables installed in the garage?

At €500 and a "reasonable budget," I would definitely skip the cable...
You will surely be able to invest the money even more wisely 😉

It is a contractor electrician.

I will speak with the electrician again to make sure he charges the same price as for the house.

In the house, CAT7 costs 250€ (around $270).

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

Is it useful there?

You need to ask yourself whether it is worth $250 to YOU. None of us know your budget, your income, your hobbies, or anything else. That’s the challenging part about building a house: decisions, decisions, decisions.

Ask the shell contractor to install an empty conduit (black corrugated tubing) from the utility room through the garage slab. This will give you flexibility to later pull through a power cable as well as a LAN cable.

Well, if you’re asking so persistently whether it makes sense, you probably can’t really imagine if or how a connection is needed there. So it seems it doesn’t make sense to you. Unless you want to upgrade the garage to hang out inside and drink beer among hobby equipment. That’s still quite common in the Ruhr area, even with a detached house next to the garage.

Wow, 250 per LAN connection inside the house is quite a steep price. Now it’s too late, but it would have been better to improve the construction specification rather than later upgrading at exorbitant costs. Just using corrugated conduit as mentioned above is probably fine. However, the concern is likely about the penetration points (air and water tightness, warranty) of the building envelope, which the electrician is either “afraid” of or wants to charge a premium for. It’s also possible that this is extremely complex due to a special wall construction, and in that case, the high price might be justified.

That said, there’s a significant difference between Simplex and Duplex cables that can’t easily be explained (how high is that difference?)