Do you need LAN cables in the garage?

No patch panel is needed in the garage.

The patch panel goes in the basement. In the house, we have installed 4 Cat duplex sockets.

= 8-port patch panel

Now the only question is whether we still need Cat in the garage or not.

If yes, we would need a larger patch panel, the 12-port one.

I always get creeped out when I read about the E-installation in GU builds. For me, it would be a deal breaker if I couldn’t decide something like that freely. But whatever. There are more important things in life than LAN. Also, nobody here can guarantee whether the WLAN coverage in the garden is sufficient. It depends on too many individual factors.

For example, I have the HD Flex from Unify in my living room, only 3m from the outside wall, but the garden coverage is poor. That’s why an additional outdoor WLAN access point will be installed soon (spring). At the moment, I have a temporary one on the kitchen table that is somewhat better positioned and also covers the garden.

I always get creeped out when I read the electrical equipment for GU constructions. For me, it would be a dealbreaker if I can't decide that freely. But whatever.

The consequence would have been that we still wouldn’t have a house :/

To clarify again:

I spoke with the electrician earlier and as a goodwill gesture, he is charging the same prices in the garage as in the house itself.

CAT Simplex €190
CAT Duplex €220 both net

The patch panel prices remain the same.

I currently have 5 CAT Duplex outlets planned:

1x living room
1x children’s room
2x studio in the attic for gaming corner (Xbox) 1x Cat Duplex and in the other corner 1x Cat Duplex for desk
1x Cat Duplex

= 10 connections = 12-port patch panel

I am considering whether to install only Simplex in the garage and also only Simplex at the desk to reduce the patch panel to 8 ports.

To save about €150 on the patch panel.

What would you say we should do?
Take all 5 Simplex and the 12-port patch panel, or no garage at all, or desk and garage only Simplex to get the 8-port patch panel?

Here is an example from me.
We have everything duplex. (So from now on consider everything double)
Kitchen 2x
Living-dining area 4x
Guest/office etc. 2x
Bathroom ground floor (Radio) 1x
Bathroom upper floor (Radio) 1x
Children’s rooms 1 & 2 2x
Bedroom 1x
Garage 3x
Garage outside 1x
Terrace 1x
Hallway (Doorbell) 1x
Utility room 3x
Fiber optic between ground floor and upper floor

I think hardly anything more is possible, but as my electrician always says, "Having is better than needing" and I have the advantage of NO builder constraints.

PS. Actually, we only surf the web or look something up. Not gamers or streamers

I think with the umpteen LAN sockets (in every room!) we are moving a bit away from the OP's goal:

I would say our house is low-mid budget.

In the mid-range area, I would provide a LAN socket for the living room (TV) as well as the children's room, bedroom, and office. Access points can either be plugged into one of the rooms or have an extra socket installed in the hallway. Bring everything together in the technical room. With that configuration, you will probably have 80% of the sockets unused because phone, tablet, and laptop connect to Wi-Fi anyway. In the cheaper range, you can save accordingly on everything where no access point and no TV are connected.
I would only have a connection laid to the garage if you actually have a use case for it in the near future. You can do it just in advance if money is no object. I would not do that in the lower price range. There is radio also classically over broadcast, and most people today already own a speaker that plays music from the phone... ad-free and what you actually want to listen to ;)
Regarding the wallbox, by the way, I would wish for a model without internet connection. What is not connected to the internet with its bare backside cannot be hacked. And remote control by network operators is also way down on my wish list

Here’s an example from me.
we have everything duplex. (So consider everything below as double)
Kitchen 2x
Living-dining area 4x
Guest/office etc. 2x
Bathroom ground floor (radio) 1x
Bathroom upper floor (radio) 1x
Children’s rooms 1 & 2 2x
Bedroom 1x
Garage 3x
Garage outside 1x
Terrace 1x
Hallway (doorbell) 1x
Utility room 3x
Fiber optic between ground floor and upper floor

I don’t think you can get more than that, but as my electrician always says, “Having is better than needing” and I have the advantage of NO developer obligation.

PS. We basically only surf the internet or look something up. No gamers or streamers

Seems familiar to me even though it was "a little" more for us :p

That's not that much:p
In the garage, I would at least lay a LAN cable for an access point. That way, you can supply charging stations, speakers, car music, etc. via WiFi.