Procedure for garden planning for new construction?

Regarding the elevations: The house is currently 83 - 87 cm higher than the south garden. Due to the terrace and the 2nd level, we expect ~40cm terrace construction, meaning there remain 43-47cm that need to be filled. For this reason and also for flood protection, the sandstone wall is at the south boundary. Towards the north at the back, the property rises slightly again. Here there is only about ~50cm difference in height, which, as mentioned, we would probably leave as is and level with steps on the west side of the house. The driveway, however, will not be that simple either. The garage is about 34cm lower than the house. In front of the front door, 2 steps are also planned. Towards the southeast (grass pavers), the driveway must therefore slope down slightly (~53cm). Directly in front of the garage, about ~40cm must be supported towards the path and sloping southwards. How can this be done? Should a professional do this? Not a very simple matter, right?

I just thought of something else regarding the barbecue area: it should be framed with sandstone blocks (somewhat circular) – among other things, as a seating wall.

And the children's play area as well. I also thought of this: can bark mulch be laid in the play area if it gets little sun, or is that rather bad because of the moisture?

Now again the exact details of the heights

I think the garden is great!
In the north, the one for the kiddies, in the south for you.
I would decide on the barbecue area later based on the location and gut feeling.
I would plant the two small grassy patches by the utility room with simple vegetables - for harvesting, of course.
What I miss is a place for dead branches and compost... for that, if I were you, I wouldn’t plant shrubs too close to the edge at the border, so that the waste can be disposed of behind them. Access via a beaten path.
Between the parking space and the garden, provide vegetation with autumn colors. When you arrive and have to go from the house, you just have to capture the autumn foliage and coloring of the Indian summer.

Definitely hire a garden landscaper for the different heights. You can do the paths and individual beds yourself. Don’t forget the foil under the gravel.

But overall, just don’t be too picky – nature will take it back anyway.

Attached is our current plan (with approximate measurements) of how the final result is supposed to look. [...] Can we still improve anything or do you have any suggestions for the design? Is everything in the right place? So, what would you start with? What can be prepared?

First impression: Great! I would try to reduce the number of lawn areas, for example, the rabbit hutch could also be placed in the corner of the utility room/garage, then there would be space on the left edge of the property for shrubs or a kitchen garden (berries ...?). The strip on the right is of course somehow a pity; how often is the path used? Maybe you could also create a meadow+flowers there instead of "standard lawn".

Thank you. I'm glad. Unfortunately, the rabbits have died in the meantime, so they don’t need to be planned for at the moment. That means we will probably plant more bushes along the border with the neighbor. What could be planted in the north corner (house/garage)? There is almost constant shade here. We had considered maybe creating some kind of second terrace or seating area along the garage wall towards the shed at some point, so for now we have only planned lawn here. But maybe shade-loving plants and climbers could also be planted here? Or would you suggest building a seating area with a gravel base right away? We will create a revised plan with a few ideas and tips from you.