Floor plan design single-family house with around 150 m²

And then everything is built around the chimney, which probably won't fit into the budget anyway with the pressure monitor and so on?

If I were you, I would try not to lose focus and create a definitive written room program. This fickleness can silence even the most patient user here. @kaho's patience is remarkable. Actually, it’s needed in another discussion [emoji12]

I didn’t actually want to come across as so fickle. Maybe I wasn’t clear enough in my initial description. But sometimes things develop, suddenly other things become important when you think more about them. That’s how I would describe it, it’s a process. But I didn’t want it to come across as if I have a different opinion every day...

Since the house was quite cheap at the base price, I hope there is still enough left for extra features like a fireplace, etc. I prefer to invest a bit of money in the interior, where I always live, rather than on other frills.

I am still amused how, on the one hand, the chimney of the cozy fireplace receives attention almost close to idolatry, while on the other hand, no chimney flue is intended at all for the actual heating

I always thought that was an architect's matter, and that it is then placed somewhere nearby/in the utility room?

Well, I haven't read anything about a gas heating system or the like. For example, we have geothermal energy. That doesn't require a chimney. Maybe OP is planning something similar.

A gas heating system is currently planned. If the architect doesn’t convince us with good arguments for something else, it will probably stay that way.

I always thought that was the architect's job, and that it then goes somewhere near/in the utility room?

Well, then you could actually just plan the interior walls, and the exterior walls would be the architect's job.

But of course you can do it that way: the client just draws what is emotionally important to them, and the architect does all the technical trivial stuff.

Only, if you're already at it and also visualizing details: I would want to see "the whole thing" – but that is indeed a matter of taste, and you can have a different attitude about it than I do.

A gas heating system is currently planned. Unless the architect convinces us with good arguments to choose something else, it will probably stay that way.

Well, in my opinion, the chimney for the heating is actually relatively stress-free, as it can go through the utility room and then probably through the bathroom near the gable without major difficulties.

Well, in my opinion, the chimney for the heating is actually relatively stress-free,

I also don't fear that it would cause stress. It just reads a bit odd to me to put a lot of thought into where the second chimney breaks through the roof on one hand, and at the same time to not care at all about the first one. It seems sensible to me to bundle the flue pipes into a common chimney (not at any cost, but at least to have that on the radar, that you coordinate it).