Orientation of the house and garden towards the east

What is important to you? Are you the type of sun worshiper? Do you want sun all day and especially from the afternoon to the evening in the garden and in the house? If that is very very important to you, this is probably not the right property for you. Personally, I would even prefer it that way, but in the end you have to see if it suits you. If that is too big a compromise for you, then better leave it.

And isn’t there some website somewhere that calculates the position of the sun? I mean, I read something like that here in the forum once,

The solar altitude is 64 degrees. Then at a distance of 6 m you have about 12 m height. The terrace could be in the shade. The house is not.

I went there again just now. I think we’re rather not going to take it. My wife believes she wouldn’t be happy there. On the one hand, the house's shadow comes from the south, on the other hand, if you look at the wall, the shadow cast already extends quite far forward. At the neighboring house, there is basically a strip about 1.5-2 m wide from the wall with a little sun (around 3 p.m.), after that it probably casts a shadow. In the morning it was also shady (I was there yesterday between 9 and 10 a.m.). It’s actually a shame, since it was the first good offer in months. On the other hand, I’ve now also heard a few not so great things about the provider. He said one could move in within 12 months of purchasing the plot. Apparently, the lead times at the prefabricated house manufacturers are currently around 2 years. But that is probably just normal sales-promoting talk.

hm... it's February!
It looks completely different in the summer!
But if there is a bad feeling, you don't have to force anything.
Otherwise, I actually wanted to take a look at the floor plan, how much reaches the house.
And start here, because the drawing is totally confusing.

is the house the right size? You are not allowed to build that big, right? In case the same thing comes on the plot again.

You really don't know if you have already dealt with Sonnenstand Punkt de and everything. The initial question, whether it is dark, is a bit confusing. Nowhere in the garden is it basically dark when the sun is shining. Not even in the north. It is just different: diffuse light.

Then better leave it if that bothers you. That is important, and after all, you are not buying a sack of potatoes but a house where you usually stay for decades.

My wife believes that she will not be happy there. On the one hand, the house shadow comes from the south, on the other hand, if you look at the wall, the shadow cast already extends quite far forward.

You actually don’t need any factual reasons anymore if the wife has doubts (or the dog growls). Then it is in any case wiser to give other alternatives a chance.