Old building or new building?

Well, maybe you should first look around the real estate market for motivation, see which costs arise from both buying existing property and new construction, and then you might gain much more enjoyment from sensibly expanding and using what you have. Because I don't find your current income situation convincing enough to create a reasonable situation with the 3000 Euro/sqm living space you mentioned.

You seem to be debt-free now. And I would pick up on the tip that has already been given here, to calculate a proper valuation for your existing property and then compare it with buying/new construction. Then perhaps also

Now we don't like it at all...

what you haven't explained in more detail so far.

Well, maybe you should first motivate yourself by looking around the real estate market, recognizing which costs come up for you both with buying existing properties and new builds, and then you might gain much more joy in sensibly expanding and using what you have. Because I do not find your current income situation convincing enough that, given the 3000 euros/sqm of living space you mentioned, a sensible situation would arise.

Now it seems you are debt-free. And here I would pick up the tip that has already been given, to determine a proper calculation for your existing property and then compare it with buying/new build. Then perhaps it will put into perspective

what you have not explained in more detail so far.

The situation with neighbors on three sides is more than annoying... You have zero. Zero privacy...
Furthermore, almost all rooms in the house are so small and cramped that it becomes difficult with the bathroom. For that you 'have to' add another floor! Then install a complete central heating system...
And all that while living in the house...
Also, it would probably cost a fortune to get the street blocked off, with the school and buses—believe me, I have already thoroughly inquired and thought about it...

Besides, the house is on a busy thoroughfare. Opposite there are 3 schools. From 7 am to 4 pm it’s a real hustle and bustle with easily 8 buses in front of the door, etc.

And take all that on if you don’t feel comfortable?
I already understand that the new build is not so easy to do just like that...

So first of all, the question is how you come to a decrease in real estate prices.
Then you simply have too little income for a purchase or new build in your region. Even in the worst location in Germany, it gets tight, even if the land is given away.
Equity capital is of course good through the inheritance. Your semi-detached house will probably only be sold significantly below value due to the incomplete renovation.
You are reaching for the stars without even having the necessary capital to any extent. Whether grateful or not, the only alternative would be an affordable condominium. Maybe with a garden share. After selling the semi-detached house.
Or massively increase your income.
I would renovate completely anyway.

No one in my circle of acquaintances earns, as is apparently common here in the forum, €6000 net.... Still, 80% of the people have built houses in the last 3 years!

&
Here in the area, houses with the key data of our house are sold for far more... I can't comprehend it either but apparently there is demand...

Or massively increase income

What massive income is being talked about? For example, in the case of a family of three?

When I look at the area and use your mentioned 320k as equity, I would talk about ~4000€/month to get into a reasonable range. What other people often forget to mention, by the way, are e.g. inheritance, family grants and so on. So don’t look left and right, but focus on yourself. With 2500€/month plus equity, I would look for properties up to a maximum of 450k.

If I look at the area and assume your mentioned 320k as equity, I would talk about ~4000€/month to get into a reasonable range. What other people often forget to mention, by the way, are e.g. inheritance, family grants, and so on. So don't look to the left and right, but focus on yourself. With 2500€/month plus equity, I would look for properties up to a maximum of 450k.

OK, your numbers actually sound totally manageable and realistic to me!

Let's see what time brings.... Realistically, existing houses up to 450k would definitely be possible.. Also doable with own contribution. Moreover, we are now at least putting away 500-700€ every month again... Depending on what we keep investing here again and again, sometimes more, sometimes less..