New construction: approximately 280m² plus basement - your suggestions

Unfortunately, it is not mine either. I find it quite old-fashioned with the small windows and dormers.
Now, about the floor plan:
The utility room, is it now a cloakroom or technical room? Something is missing there. Where do tools, waste paper, and bags go? Where do the jackets, the entire wardrobe of 5 people go?
The utility room upstairs is probably for laundry? I would miss a window there – natural daylight!
Storage space is overall a bit scant.
Kitchen island twice as long and turn it 90 degrees.
If I were to inherit the house, I would put the wing in the bay window, the kitchen where the wing is, and the living room where the kitchen is now.
The bathroom upstairs will be very dark.

Attached is a typical house from the area.

We have the basement as storage.

In the common room we only have and need a display cabinet for dishes.

The addition is the nicest room to do that.

The kitchen now also has a view of the street, so you can still see when the Amazon guy comes.

Thanks for the picture. Is that a new building?
In your house, the small windows of the bathrooms and the kitchen are way too small. They should be adjusted to match the others. How wide are they? I would plan all of them a notch bigger. (Or two notches.) It doesn't make sense if all the rooms become gloomy.
I would keep the shutters... but leave out the round shapes...

Ah, okay... the vacuum cleaner is in the basement... or what else would be in the basement besides the technical room? I would plan a built-in closet on each floor in the hallway for cleaning supplies and such.

You have to be careful that such a large room doesn't feel uncomfortable. Furniture is what makes a room a living room.

I have a different opinion. In such a glass extension, one could also feel somewhat out of place "in the garden." Looking outside is one thing, going outside when the weather is nice is another. You can quickly feel unprotected in a house annex.

The mistake many make: you don’t stand bored at the window staring and staring. Maybe consciously once briefly. You have daily tasks to do. If I'm waiting for the postman, that time is used for quick weeding in the front yard or cleaning the mailbox.

A huge problem you will have is the budget: I overlooked the basement... with the basement and all the Palatine frills plus sauna, extension, size, 3 bathrooms you will be above 900,000. What did the architect estimate??? They go by cubic meters; that should be even higher, right? Then add the 20% that an architect’s house generally exceeds the budget by... that's already a fortune.

I think an adjustment of the living space should be approached realistically!
And if I don’t write it, then who??? :p You could easily take a meter off across the lower third without the house losing much. Living area a bit cozier, hallway and bedrooms upstairs not swollen, children’s room and bathroom in the attic.

OK, the house also has nothing to do with the picture in my head. It also seems a bit mixed up without the multi-family house character.

1. Question: your budget is very tight. Can you add some extra if necessary?
2. The TV room is the study on the ground floor, right?
3. The example has undergone several changes. Without a balcony, without a conservatory, it definitely has something. Clearly overloaded. The builder already showed back then that he can afford something and ensured plenty of separation.
I would carefully consider which elements you like. Take the round window. In the example it stands out, for you, well, it has to go in.
Without looking at the plot more closely
Pro arches, but the shutters off

I would separate the garage from the house. Small gable roof on top and the round window in the gable. Two small gates instead of one large. Arches over the gates

Roof terrace on the dining room extension. On the upper floor on the garden side large windows with arches like on the ground floor. The loopholes would be too small for me.

Street side
Remove shutters, windows with arches
Door differently. Imagine the old doors to storage rooms. Arched, double-winged, wide enough for a wine barrel to pass through, wood. I would adopt the dimensions and the arch. Fill with glass and door.

On the gable sides windows with arches

The roof with the mini dormers is disturbing. Skylights don’t fit.