ᐅ Which is more suitable for the site conditions: a basement or a slab foundation?

This might sound a bit unusual, but you are always the first person responsible for something like this. It is your soil survey, and you are commissioning it for your property. The soil survey has relatively little to do with the contractor carrying out the work. You need to understand what kind of soil it is, how load-bearing and permeable it is, whether there are rocks, and so on.
If someone offers to handle the billing for it, in my opinion, it is just an attempt to get you locked into a contract.

In my view, the drainage planning is the architect’s responsibility. But again: this is your project. If they forget about it, you have a problem, not them.

Depending on how much time the officials have, you can of course ask questions before starting construction. It is helpful to be very specific. In our case, you can submit a preliminary inquiry online. This is free of charge. Since we are a small municipality, I can also approach our head of office directly.
Hopefully, your architect can answer all of this as well.
By the way, a prefabricated house on a slope wouldn’t be my first choice.

Thank you for the explanations. So, under the given circumstances, you would proceed with a traditional approach using an architect for design phases 1-4, and then continue either with the architect or a general contractor for phases 5-9?

TobsBAU schrieb:

I am in talks with a prefab house supplier,

Prefab house supplier because of the common misconception that they are the first choice for more accurate final price estimates?

TobsBAU schrieb:

where the foundation slab, etc., is included in the fixed price.

The foundation slab should definitely be included in the offer, if only because it is part of the scope of work of the (shell construction) general contractor. Without the foundation slab, nothing else matters—it is literally THE base. Additionally, the main building level is the root of all critical interfaces.

TobsBAU schrieb:

I was offered to have the soil report prepared in advance (cost covered by me, 1500 € (approximately 1600 USD), deducted from the contract sum if commissioned). After the evaluation, a fixed-price offer for the shell construction would be created. Would that be a feasible approach, or should I commission it independently and individually?

This is a test of your ability to think critically, with a little bit of lubrication added just in case.
Your plot is the same for every contractor. Always commission the soil report yourself. I already deliberately advised you to perform a broad screening of the entire buildable area (including near the edges to capture homogeneity), because doing a new one for every specific house footprint ("retract that command!") would be nonsense.

TobsBAU schrieb:

So you would under the circumstances build in the traditional way with an architect (phases 1-4) and then continue with an architect or general contractor (phases 5-9)?

Although I was not directly addressed with this question, I gladly give (and did already give in “A building guide for you too: the HOAI phase model!”) the generally valid answers: always a self-chosen independent architect, NEVER phases 1-4, phase 9 also total nonsense for an owner-occupied single-family house, but rather:
1. Phases 1 and 2 (called “Module A” in the building guide)
2. Rest period (usually with a decision point, here I would leave out all the wood experts and only consult 3 or 4 masons)
3. Phases 3 to 8 (= Modules B and C) preferably with the same architect (note: 3 + 5 = 8).
And for the general contractor, my eternal refrain: “generally happy to work with one, but never without a proper tender.” The mistake many owners make, assuming from the balanced scorecard that they can safely commission it as a black box, is a costly hobby.

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TobsBAU schrieb:

So, you would build under these conditions traditionally with an architect (service phases 1-4) and then continue with either the architect or general contractor (service phases 5-9)?

The question should rather be: what would I recommend for you? I definitely agree with @11ant. On a slope, I would generally advise against using a prefabricated house supplier. They usually just place their building on the finished foundation slab without considering all the other aspects of your slope.
A general contractor (GC) is better because there are usually committed and professional people. If they are local, they have probably already built one of those houses on slopes, which I would consider a basic requirement to ask about, including references. Planning the outdoor area is typically not an issue for a GC. As long as everything is paid for, you can usually get a well-rounded package.
Most likely, I would recommend working with an architect on a slope. The advantage of an architect is the focus on planning. A GC often only delivers average results because they often employ mainly draftsmen.

If it were my project, I would definitely start with an architect and go through at least phase 2. This would allow me to first check if the project has potential. If so, I would continue with the architect up to phase 5. Since I have quite a bit of experience and several trades are more or less constantly involved in our projects, my approach from that point on would probably be different from yours. I would leave some work to the architect but take over most trades myself from there. However, I would not recommend this for first-time homebuilders and strongly advise continuing with a professional. You can also combine both approaches, for example, switching to a GC after phase 2. But that is something each person needs to decide for themselves.