Two-story single-family house without a basement with an outbuilding and driveway to the south

We would never give up our fireplace; its regular use for heating purposes was even a decisive parameter in our construction project.
In connection with a technically inherently slow underfloor heating system, I see it as something to be individually evaluated to what extent this can work for me. For me, it was always much too warm, and I partly had to basically heat out to avoid it being too warm.
Basically, though (without underfloor heating), my recommendation would always be: Go for a fireplace! Maybe I am mistaken or can only report from my own experience with underfloor heating.

Especially with the slow underfloor heating, I find a fireplace useful and great. That’s how we have it, and I wouldn’t want to miss it. The underfloor heating is set to 21 degrees, which is perfect for us during the day when you move around more or are not at home at all. But in the evening, it’s too cold for us. Then the fireplace comes in, and it sometimes gets to 24/25 degrees. That is perfect for us.

The federal state would be Lower Austria, but only OE was available for selection

I was recently repeatedly in Sopron, my mother’s former home. Vienna has meanwhile become our favorite airport.

Especially with the sluggish underfloor heating, I find a fireplace sensible and great. We have it like that and I don’t want to miss it. The underfloor heating is set to 21 degrees, which is perfect for us during the day when we move around more or are not at home at all. But in the evening, it’s too cold for us. That’s when the fireplace comes in, then it’s sometimes 24/25 degrees. That’s perfect for us.

Okay, I understand that there are other perceptions out there. I can only speak from my own experience, although I must say that any type of heating has its advantages and disadvantages.
For me, it was simply that during the day it was at a normal temperature (maybe 21 degrees or so) and as soon as an additional heat source came in (e.g., sun) I had to open the window; a fireplace would have raised the otherwise existing normal temperature by at least 1-2 degrees and that would have been too much for me, as I don’t like “too much” heat.
Maybe it’s also the case for me that I don’t move more or less during the day than in the evening and therefore it makes no difference for me. But it’s good that the OP can look at and explore different points of view and sensations.

The federal state would be Lower Austria, but only OE was available as a choice

Yes, but then you mention that in the initial post that the German rules do not apply.
Then forum members can adjust accordingly. You are not exactly exceptions, but different laws simply apply. I will get back to that.

therefore only very small as an emergency shower, so to speak

If you want to have a shower there later, or even already lay pipes, then it should also work later, and in a size that someone with a height of about 1.40 m and taller can shower there. It’s no use exchanging the “emergency” in the shower with a “micro.” On the 180, a toilet and shower with 90 cm each just fit, luckily that still works.

The sauna thing is probably a matter of interpretation by the municipality – however, a bathroom is explicitly listed in our building regulations as a possible room use in the outbuilding since it is not a living space. But this is probably regulated differently in every federal state.

No, that is not a matter of interpretation. It may not be a living space for you, nevertheless no auxiliary facility with a burner unit/burning place/fireplace may be located on the boundary. See Lower Austria Building Code.

I re-read the building code, in our case only a maximum built-up area of 100m2 and building height of 3m applies for the outbuilding –

I would check that again. Have you read the generally applicable Lower Austria Building Code, the garage ordinance, fire protection, or neighbor law? Or whatever else you still have?
As I said: the sensible laws are similar between the states.

I don’t really care where you put your sauna, but if you are planning your house, you should also be able to apply the laws.

their freezer room was even smaller than 5m2 and they even managed to fit a washing machine and freezer there.

What do they heat with then? Or is the freezer room not the utility room for you? Do you want to break the record for smaller and smaller utility rooms? That’s not great, to have such a tiny room where you can’t even sort laundry. Then you also want your wardrobe in there. 5 sq m is 5 sq m – about half of the optimum minimum size. It somehow hardly works, but most would rather want 5 sq m for a hallway and 20 sq m for a nice utility room so that there is space for tools, drinks, and cleaning supplies.

A new staircase changes everything.

Yes, that would indeed often be better.

How did you implement your sauna? Do you also use it in winter? How close to the terrace should it be? Would you perhaps have a suggestion where you would place it? With more info, I can probably convince my husband, because I personally like the idea better. Otherwise, so much garden space remains unused and that would be a shame.

We have the barrel sauna you mentioned. The sauna is in use at our place from October to April/May. During this period, we go about twice a week on average. We used to go to saunas outside often, but with small children, saunaing at home is actually the only option if you want to sauna regularly and together. As I said, our sauna is attached to the terrace. Normally, after saunaing, we first relax on the terrace and then go through the terrace door into the living room. You can also get from our terrace to the guest room as well as the master bedroom (3 terrace doors), so we are flexible if something changes when the kids grow older. How exactly you could implement this, I don’t know either. I just wanted to suggest with my post that I would wait with the sauna anyway until the house is built and approach it rather with the garden planning. Then you might also have a better feeling for where it would make sense. Maybe there is also a spot with a view or something else on your property...