Is a house for a total volume of 400k still possible at all?

Yes, I understand you. But 400k is nothing these days. The money isn't worth much anymore, you can see how the government handles it. Very soon, no single-family house will be possible for under 1 million, including the land. In some regions, it is already like that, but it will happen nationwide. I think at most in 10 years. The real estate market will not crash, on the contrary.

Yes, if one knew that for sure, I would increase my budget to 500k since we have at least 100k equity (depending on the sale of the current property). But somehow I am too afraid to take this step.

Afraid of what? Fear is a very bad advisor

Fear of getting into such high debt. After all, we're talking about 350-400k debt. I have great respect for that. If one of us loses their job, it might already get tight. And at the moment, it doesn't look like the economy will recover quickly from all of this.

hm so we have already thought about it. The following points are at the top for the basement:

Laundry room for washing machine and drying room
Utility room not on the ground floor
Hobby basement (workshop)
Hobby basement multimedia

I see it as almost impossible to fit all of this in a 125sqm house without a basement. It should also be mentioned that we are a three-person household. Well, as I said, we will first think about how sensible the whole thing is.

Laundry room with washing machine/dryer and drying room can easily fit into a normal utility room. You can plan that very well yourself with Ikea furniture. It is important that everything is well planned in the drawing from the start and that you look at model houses to get a feel for the size.
Why not have the utility room on the ground floor? You can also put it in the attic, but in my opinion, that causes unnecessary costs. If the larger components like electrical distribution, heating, and ventilation system are well planned, you hardly waste any space because they hang on the wall anyway. Below that, there is enough space for cabinets.
A workshop can easily fit in the garage/shed.
Typically, a standard single-family house has 2 children's rooms and one guest room. If no more children are planned, a room is free for a multimedia room. Or the converted attic.

Fear of indebting oneself so much. After all, we are talking about 350-400k debt. I already have great respect for that. If one of us loses their job, it might get tight. And at the moment, it doesn’t look like the economy will recover quickly from all this.

Don't forget that you get an asset that — at least currently — is steadily increasing in value. It's not like you are buying a company that can go completely bankrupt. You shouldn’t be afraid. If possible, the house should also be able to be carried on one income. Even if that means lowering the payment.

hm well, we have indeed thought about it. The following points are top priority for the basement:

Laundry room for washing machine and drying area
Utility room not on the ground floor
Hobby basement (workshop)
Hobby basement multimedia

I find it almost impossible to fit all of this into a 125sqm house without a basement. It should also be said that we are a household of three. Well, as I said, we will first think about how sensible the whole thing is.

You know what? Don't build! Then you will never regret it! And: now you don’t have the rooms either...