Optimize functional ground floor layout within limited space

I wouldn't do that. 2.52 is already not luxuriously much, and then reduce it significantly on the ground floor?

I also can't understand this 5x6m garage fetish. The classic garage is 3m wide, and that has been sufficient for decades.
Why give away valuable living and utility space for the metal box?

People don't constantly run through the play corridor like at a train station. There are railings to prevent falls; generations of children have safely managed stairs at home. I wouldn't have a problem letting guests sleep next to the laundry, nor setting up a home office there.
I'm not a hotel, and for the few days a year when guests stay overnight after a party because they are too drunk to go home, a folding bed next to the laundry is enough. If someone doesn't like that, there are cheap hotels nearby.

Rarely will a car even be in the garage; you'll only put it in there during the really cold season, but then you don't need the bicycles daily either. When it's warm outside, the car is parked in front of the garage and the bicycles are easily accessible inside. This is one of the reasons why I fundamentally consider a garage pointless. A carport with a shed works just as well.

With the garage, which is inside the thermal envelope and therefore complex and expensive, you effectively give away almost 20m². For a metal box that is built by the manufacturer for that purpose and tested in the desert and northern Sweden to stand outside day and night...

Especially now at -10 degrees, I wouldn't want to be without a garage. I now always watch my neighbors in the morning who have filled their garage and now have to scrape for minutes. That is no pleasure.
And one more thing about the 16cm above ground level: Is that technically necessary? If not, then I would definitely forgo it. Not only because you always have a bump to drive over at the garage (the tires will be happy), but also because it is a tripping hazard (especially for children) and you can improve the currently rather low room heights. Because 2.52m is already the minimum to have a nice sense of space. Except in the garage floor, there I would plan the 2.3m from the attic floor. So that you then have on the ground floor: 2.3m, upper floor: 2.52, and attic: 2.68. Because especially in the living area, having a ceiling height of only 2.3m (in such a large room) would completely destroy the sense of space. You almost have to be afraid of constantly having to duck your head. It's a mystery that an architect would plan that in such a house. Walk through a subway underpass (which should also be about 2.3m high and 12mx6m). It crushes you so much that you definitely wouldn't want to live like that in your own house.
And in my garage, I always park forwards. That works wonderfully and you can comfortably unload the trunk even if two cars are inside. That is not possible when parked backwards. I also hardly know anyone who parks backwards in a garage. Your garage is large enough without any problems.

You park backwards so that you can drive out forwards. Important when the sidewalk is directly in front of the garage (if I understood the original poster correctly, this is the case here. This also eliminates the need to build a carport in front of the house) or if the area is otherwise poorly visible. In this case, the point is also that the door is on the right side, meaning if you park backwards and keep to the far right, you can comfortably get out and walk to the door. Driving out forwards is not as comfortable. Regarding ceiling height, don’t let yourself get stressed. Many millions of people live with 2.30-2.40m and are happy with it. You just shouldn’t put wooden paneling on the ceiling.

I would like to point out that a room measuring 3x4m with a ceiling height of 2.3m feels different than a room measuring 6x12m. In such a large room, it feels very oppressive when you stand at one end and look to the other. In smaller rooms, ceiling heights of 2.3-2.4m are not so bad. After all, millions also live well in their new-build apartments.

We had a ceiling height of 2.30 m in the old house and I already found that quite oppressive. Now we have 2.49 m, which is okay. What comes to mind about the floor plan: I wouldn’t want a living floor without a WC. Normally you have the guest WC there, which you can use yourself as well. But running up and down the stairs for every toilet visit?