Garden design new build end-terrace house

Does the neighbors' planting really help much since they are one meter lower?

At our place, the neighbor's property was indeed lower back then, their bushes were transparent on the slope, but for a nice view from our terrace, it was enough for us to look at this neighboring greenery. We actually only put up a transparent wild fence.
With this house, you have to see what you want and what can actually be achieved. The neighbors "back there at the main garden" will - if they want to - always be able to look in. But it’s not about creating a nudist garden, rather just a simple feeling of security in your own area. I would also plant something on the left side. But the whole upper side: what should you plant there now as a “hedge”? That would only take away garden space but change nothing. You also have to keep distances with the vegetation, meaning planting at least 50 cm away from the boundary, which then takes at least one meter from the area.
I would also put up some kind of espalier opposite the side window and let it be covered with climbing plants. That does not take up much width and allows passage.
I would replace the apple tree with a more funnel-shaped tree (e.g. maple) and rather work along the side boundary with espalier fruit plants.

On the narrow side, I would install trellis and climbing plants as a privacy screen. Clematis, Virginia creeper, etc., are also native.

Naturadb provides information on which plants are native or neophytes, and how ecological they are. It also gives suggestions if you, for example, only look for climbing plants.

Raised beds in the front garden, why not. Is it sunny there?

First of all, many thanks for the previous answers! To keep it clear, I will partly answer without quoting.

Terrace slabs are 60x60x2 cm porcelain stoneware on grit.

South-east is at the bottom of the plan, so the terrace is oriented accordingly to the south-west.
At the top of the plan are multi-family houses. They have been there for a few years already, so I don't expect many more plants there. Quite a lot is already growing there, but 1 meter lower than our garden, so it offers little privacy. This is clearly visible in the second to last picture. The tree there is right in front of our large window on the long side of the house. Here is a photo from the inside so you can better imagine it:

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Also a question related to that: what do you mean by "Pergola in the max. allowed height for direct border contact and then green it"? A pergola is a roof structure, right? Could you post a few examples?

On the left side of the plan is the garden of the house currently under construction, so we can actually wait and see what they plant there first.

Small plots are usually designed so that the diagonals work in your favor by being longer than the plot depth itself. So go along diagonals if you want to create a bit more “space” through sight lines,

Unfortunately, I don’t understand this. Can you try to explain it differently?

Modern is already the clean lawn area.

Yes, it is, but I’ve also read that gardens with only lawn tend to look smaller. Hence the search for a bit of inspiration.

In our neighborhood, nobody cares because border distances are not practical. But I don’t know your neighborhood.

At least on the long side, it matters less here too because of the multi-family house. Our construction fence stood in their garden for months without bothering anyone.

We then actually only installed a transparent wild fence.

Can you show me a picture as an example?

Espalier on the long side of the house is a good idea. Always happy to post a few example pictures. Especially in the beginning, when you’re not familiar, that always helps me figure out which direction it should go. Thanks therefore for the tip with Naturadb!

In the front garden there is sun until noon and then again in the upper right corner of the plan in the evening.

A quick question about that: what do you mean by "Pergola at the max. allowed height for direct boundary contact and then green it"? A pergola is a roofed structure, right? Can you post some examples?

I mean a fence with a top part that can support plants. This way, climbing plants can be used as a privacy screen in a relatively narrow space.

was that you with the wooden cellar? Or do you know which user that was? They had a very small plot and I think it's a good solution in terms of privacy screen, terrace, and planting. It might be a good inspiration for the OP for the narrow side strip.

This is a trellis/pergola - you can also pimp it in a modern way