Designing a garden on a slope sensibly

I would have said yes, but others are more knowledgeable about that.

But that's actually not how you want it according to your opening post.

How did you imagine it?
There must have been some thought processes during the planning. How do you envision the garden in your imagination?
Your parents have dug out, right?

Where is south?

You won't get by without terraces. It's just a question of how and where, and I would say they need to be established parallel to the house construction.

How is your neighbor building on the other side?

Tricky situation.

You need a path to the garden
You need a terrace and a play area level and preferably at the same height
You have to compensate for a large height difference to your parents without your parents looking at a wall
Do you have restrictions on what and how much you have to plant?

I would have said yes, but others know more about that.

But that's actually not how you want it according to your opening post.

How did you imagine it?
There must have been some thought processes during the planning. How do you envision the garden in your imagination?
Your parents have excavated, right?

Where is south?

You won't get by without terraces. It's just a question of how and where, and I would say they have to be planned parallel to the house construction.

How is your neighbor building on the other side?

Tricky situation.

You need a path to the garden
You need a terrace and a play area level and preferably at the same height
You have to absorb a large height difference to your parents without your parents looking at a wall
Do you have any requirements on what and how much you have to plant?

My parents have excavated, like many others in the new building area. But we don't really want that, or rather, due to the basement construction, we are subject to very different conditions.

We have a 3D model of the house and property, which I took a photo of and attached. Maybe you can see well on it how we imagined it. On one side are my parents, on the other side we have no neighbors and will never have any, at most a field path will be built here.

I wouldn't have a problem putting the house on a plinth and then absorbing the garden towards my parents. That would probably be the easiest solution, so that you have a ground-level terrace and play area across the width of the house. The question then is how to design the area toward the parents. Terraces? Slope?

We don’t have any major requirements. Embankments toward the street must be planted, but that does not apply to us. And one tree must be planted.

You have to compensate a large height difference to your parents without your parents looking at a wall

A nicely designed 150-high wall can also delight. It does not take away the sun from the parents in the southwest either. If they stand on dry stone walls, you could tackle the project together. I wouldn't worry about the height: they are your parents. And if the wall turns out nice, no one will measure it again in 30 years.
Make sure that from the driveway to the high garden you get a path with lawn and not just stairs, so you can also move wheeled equipment there.

I hope for constructive solutions, but so far I have only received them from @haydee. Shame.

…. Because she has such a garden. For others, some info or measurements are missing for the theory.

A nicely designed 150 cm high wall can also delight. It won't block any sun from the parents in the southwest. If they are on dry stone walls, you could tackle the project together. I wouldn't worry about the height: they are your parents. And if the wall looks nice, no one will measure it even in 30 years.
Make sure that from the driveway to the high garden you also get a path with grass and not just stairs, so you can also walk through there sometimes with wheeled equipment.
... Because she has such a garden. For others, some info or measurements are missing for the theory.

Because my parents have already dug out, there is already a relatively high earth wall standing towards us. They want to terrace it over to our side. But if we now put another 1m of wall on top, the wall will be higher than their entire ground floor and will take quite a bit of light because of that. Surely that's the easiest option and if it were any neighbors, I wouldn't care, but I'd like to grant my parents some sun because they're already sitting deep in a hole from the digging :D

I've attached a picture. It’s a bit misleading, but in the back corner it’s also 3m. Adding another meter on top is, in my opinion, somehow unpleasant...

The 3D model is printed out of reality. That’s how it becomes really expensive.

My parents have, by digging down, already created a relatively high earth wall towards us. They want to terrace it over to our side. But if we now put a 1m wall on top of that, the wall will be higher than their entire ground floor and will take quite a bit of light. Surely that is the easiest option and if it were any neighbors, I wouldn't care, but I would like to give my parents some sun because they are already sitting so deep in the hole due to the digging :D

I attached a picture. It is a bit misleading, but in the back corner it is also 3m. Adding another meter on top is, in my opinion, somehow ugly...

How do you come to that conclusion? It is primarily about the house, not necessarily about the garden. The only thing that according to the development plan definitely has to stay as it is are the steps next to the house.