Our floor plan... please help with optimization.

No, I meant more that you should consider something like that because otherwise it might get warm in the summer and a covered terrace does have its advantages. Next try:

So it exactly meets our expectations... But is 7 sqm utility room enough for air-to-water heat pump, washing machine, and dryer? Difficult... The idea with the roof is not bad either.

7 m² should be enough for technology and laundry. Additionally, there is the storage room under the stairs for the vacuum cleaner and co. However, you might have to do the ironing in front of the TV or in the office. You need to create storage options on the property for stuff that is otherwise stored in the basement. Kitchen things should fit well in the kitchen – it is already large (so it has many cabinet elements).

Okay, we will sleep on it for a night.
Thank you for the great help!!!

I would make the entrance area bigger. It's already better like this, but with children a lot can really end up lying around there. Also, I would integrate a shower into the toilet on the ground floor. That takes up a few square meters but saves stress when the children are teenagers.

If you skip the dressing room, there would be space for the office upstairs. Or you could place the washing machine elsewhere and make the utility room smaller.

Version with larger utility room and entrance area. However, here the kitchen, dining, and living areas are very open (unclear whether this would already be more expensive structurally).