Is a penthouse feasible for 350,000€?

I can say from experience. That was possible 20 years ago, but rather not today.

You cannot cut out that many of your wishes.

I doubt that this was still easy 20 years ago, so in 2005. We are more likely talking about 1985, so 40 years ago or even further back...

Of course, it can still work today if you know the right craftsmen who in turn know others. But it just takes longer, and what you save on wages, you partly pay again in materials (no bulk customer prices) and double workload.

In the end, everyone is exhausted and can't stand each other anymore...

Show the slope, then one can say whether it might work without a basement and garage and some square meters less.

Maybe you can get more than just 250k from another bank.

We were thinking of a 150 sqm house

That is a manageable size. And yes, of course you have to think about the third dimension of the slope, because a slope requires a floor that is built half into the slope. However, it is not self-evident that you immediately build a third floor; in most cases that is not financially feasible, even if you have about €200,000 more available.
I question these parameters:

It would be built 2-story, with a basement,
double garage also with a basement (otherwise not possible), small sewage treatment plant
We were thinking of a 150 sqm house

Why is a house being planned that can adapt the least to a slope?
You look at the slope and see which house can be integrated there most cheaply. Hoping that about 150 sqm gross will result. Without a garage.

We would do a lot ourselves because we have many acquaintances who can help us

Helping once is something different than accomplishing something permanently. The acquaintances would have to sacrifice basically half a year of their weekends in order for you to save something. And do they do it for free then? They also have to work 40 hours per week to support their families.

both grandfathers are bricklayers, husband electrician, father-in-law painter, uncle excavator rental, etc)

The grandfathers certainly don’t want anything. But after three weeks they will also be worn out with back problems.
Ask your husband how many hours he would have to invest to save how much? Without materials. Besides his main job.

Basically, one can only say how expensive it would be with a general contractor; that would be the flat rate of €3,000/sqm, which does not even take the slope into account.
For us, the slope is initially the big unknown, the second unknown is the district where construction is to take place.
But what can actually be said: with €350,000 including incidental building costs, you will not be able to build such a house within a bank-appropriate building period.

That this was still easy 20 years ago, so in 2005, I doubt.

You are welcome to doubt. But I speak from experience. Notice the difference?

The question must be answered with a clear NO! Everything else is wishful thinking.