The same tiles throughout the entire ground floor and in the bathroom - also the same in the basement?

I would like it if you could see it from above, do you too? Then take it. You don't have to make it complicated. :) Otherwise, I wouldn't choose something too similar, it then looks like we wanted it to be as similar as possible but save money. Better to consciously combine something different.

If you look at the basement hallway from above, I would at least use the same tiles there.

So the suggestion would be different tiles in a different size?

Or in a different shade, or floor/ceiling in different tones.

What color would you see as tile in the basement? Surely a similar natural stone look makes sense, white slaughterhouse tiles would rather not...

White tiles only have a bit of that slaughterhouse vibe in 15/15, and otherwise, in my opinion, don’t deserve to be seen as popular in the same league as Aldi camouflage.

The staircase is open, i.e. no board between the steps (I don’t remember what that’s called),

Those boards are called risers.

In the basement, I would take dark gray (not anthracite) tiles from the very bottom of the shelf and definitely not spend more than 10 EUR/m² on them.

But that's just me.

If you look at the basement hallway from above, I would at least use the same tiles there.

Me too.

So the suggestion would be different tiles in a different size? Or laminate, design flooring in the basement...?

I would rather make the walls in the bathrooms (except the floors) a bit bolder – meaning different. Because it can actually become boring there.

Upstairs, engineered wood flooring is planned everywhere (3 bedrooms + hallway) and the same tiles again in the bathroom. I wonder if, for the sake of logic/sense, there should also be tiles in the upstairs hallway. How do you have it?

We have tiles on the ground floor, except in the living room, where there is parquet. And in the utility room there is wood-look vinyl; for me, tiles should have gone in there as well, but we bought the house, not built it.
Upstairs there is carpet, tiles in the bathroom. The carpet might eventually be replaced with the same parquet as in the living room.
I like having only two to three different floors in the house. To me, that makes it feel more spacious, calmer, and more harmonious.

But it’s really a matter of personal taste. :)