First of all, I think it’s good that you are dealing with this so constructively.
Before you start focusing too much on individual things and details...start from the beginning.
Plot:
Slight slope. Define that a bit. You wouldn’t be the first to imagine filling it up a bit and so on, no problem. (Slight) slope could again argue for a basement and with clever planning also a good way to bring light into the basement...a light well etc. costs a lot of money with retaining walls and so on. Also a bit of filling up. Our plot dimensions are very similar. Slightly smaller and the retaining/filling + wall don’t come for free.
Budget:
BY very high-priced. Oriented around 330€/sqm not in the super expensive areas but also different than somewhere in structurally weak rural regions in the northeast or something like that.
Your calculation with your demands will be a very tight fit!
Just a quick calculation.
Plot (including ancillary purchase costs) approx. 165k
House 160m2 x 2,500€ approx. 400k
Here in the forum people like to calculate with 2,500€/sqm. Normal standard, often plus floors + painting. No special extras. BY actually more rather.
Basement approx. 120k (especially if not just a utility basement)
Additional construction costs 50k (earthworks, connections, etc.)
Garage 20k
Carport 15k
Kitchen, furniture, lighting, etc. 30k
Outdoor facilities (slope???) 30k
Subtotal: 830k
That puts us already 30k over your budget. And partly I have calculated here with rather low values for Bavaria. You still have the question mark slope and no sauna yet, no fitness room yet, no gimmicks with electricity or sanitary, no electric blinds/smart home or anything else...Edit: Passive house and geothermal are also missing.
By the way also no ventilation. Which I would place significantly higher in my priorities than a sauna.
Yes, mainly comfort. But don’t compare your user behavior from a rental apartment (old building?) to your single-family house.
New houses are tight. Really tight. You run through three floors two or rather three times a day and open everything and later close everything again. Do you really do that every day? Or bedroom. In the new build with closed windows you feel like you woke up in a puma cage the next morning. Of course, you can sleep with tilted windows. Whether that is energetically sensible in winter...just read up on that. Sauna in the garden you can also do later. In the bathroom I see it with your budget anyway not.
So good that you start addressing this early here. My tip remains...start at the beginning. Budget and plot.