Floor plan of a single-family house with a gable roof, 1.5 stories - improvements?

Yes, that's how it is. Technology outside the house will not work! We were also told that once!

Okay. As an alternative, the bathroom could perhaps be placed on the outside between the utility room and the kitchen. The kitchen would be slightly reduced in size in the process. The hallway would then be extended up to the bathroom. You would then go directly from the utility room through the hallway into the kitchen. Bathroom, kitchen, and utility room would then also be accessible via the hallway.

Advantage: shorter & more flexible paths.
Disadvantage: hallway enlarges, kitchen shrinks. Space gain, if any, would be minimal.

Do you need the [Arbeitszimmer]?

The study is also already under review. The main purpose of the room downstairs is primarily to have the possibility later to live completely downstairs. Of course, a study would also not be wrong if there really are 2 children and the rooms are thus occupied.

The consideration would be as follows if the study is omitted: To the left of the main entrance, set back a bit, the bathroom. In front of it, space for the wardrobe. The living room would be extended around the corner up to the bathroom. The bathroom from the plan and the utility room would merge. The hallway will be extended a bit to the right so that you can get from the utility room into the hallway and possibly go straight ahead into the kitchen.

In old age, a wall could then be erected to reduce the living room and create a bedroom between the bathroom and the living room.

What do you think about that?

I find a study room really important, especially with 2 children. You also need it as a guest room. I definitely wouldn't leave it out. The ideas before were already good: bathroom between the utility room and the kitchen. We have it similarly.

Let go of the thought of deteriorating with age. Upstairs is the familiar bedroom, the large bathroom, downstairs everything much smaller. The nursing service or someone else cannot assist you in the downstairs bathroom. Separate the living room. Reduce the kitchen and dining area, where should the grandchildren go? Is the investment sum feasible? With a stairlift, the upper floor is relatively easily accessible. There is space and everything as usual. There are even lifts attached on the outside already. By the time we are old and gray, many things will be better and cheaper again.