Install a technical room in the garage? Is this possible?

OT:
Do you have a large family or will that be a conference room next to the office?

We absolutely need a large living and dining area, our family is very big and when there is a birthday we have to celebrate somewhere else every time. This is one of our primary goals with the house

To give an idea, a first draft.
Do the paths seem drastically longer in your eyes? I like that I don’t have the utility room inside the house.

Ok, it took me a while to get a clear picture of the many hallways.
How long the hot water takes to come out of the shower depends not only on the location of the utility room but also on the location of the shower and the pipe routing. Therefore, it cannot be judged based on the draft you posted (only 1 floor). Basically: the longer the pipe, the longer it takes for hot water to come out.

Regarding the floor plan itself: I find the hallways and the stairs a bit confusing. Also, you have a lot of doors. How do you get from the garage to the storage room after shopping?

I actually did not want to show a draft (it is still nothing more than that due to other unresolved issues). Tends to be, because of the slope on our property, it might become a split-level solution. The garage and stairwell at the front are on the same level to enter the house from the street at ground level, then 8-9 steps down to the basement and 8-9 steps up to the upper floor starting from the stairwell. We want to go out to the garden on the ground floor, so this was a suggestion from the architect that we like quite a bit (somewhere we have to have steps anyway). Regarding the path from the garage to the kitchen, I agree with you, but please see the picture only as a first draft, nothing more.

I didn’t want to start a floor plan discussion here either. With your explanation, I now understand it. But still, a suggestion regarding the floor plan: I would leave out the narrow hallway and make the door to the utility room at the back into the garage. This way, you can either make the garage or the entrance area larger or save unnecessary space. Because honestly, I don’t think the hallway gives you any advantage.

Are you talking about the narrow hallway by the garage (outside) or the internal stairs to the kitchen? The utility room should also be located at the basement level, i.e. lower than the garage, so that in summer you can place laundry there from the utility room upstairs (washing machine and dryer), at least that was the idea so far.