Is financing a single-family house feasible for us?

I'm with your wife, a double garage would never have been up for discussion as a saving measure. That was very important to me personally and luckily enforced in the end. You can work on things there, have a workshop, store cars and classic cars safely and dry, free from martens. Likewise, eBikes and the like are kept tidy. I would save on the garden, which usually costs between 30 to 50k. You don't need all of that right away. Also save on the fittings. Later on, you won't care whether the windows are aluminum or plastic. Or expensive versus cheap tiles. It only drives you crazy. A house is for living in, not just for looking at. Every dealer is basically a salesperson. Compare it to cars—you can start with a base price of 30k and your desired configuration usually ends up costing double. Whether you need it and want to afford it? I've always had new cars over 80k in the garage, but now my current new car costs 11k and it gives me more fun than all the others before. Perspective and all that.

We don't have much leeway if we want to be finished by retirement.

As civil servants, you will not receive a pension but rather a retirement allowance. This is a difference that should definitely be taken into account. Emotionally, you might want to be done with the installment payments by the time you retire, but objectively there is no necessity for that. I find it difficult to make an assessment. A new house is usually more than just a "residential address," so I wish your wife the realization of her claims. I personally find parquet instead of laminate good and affordable. I would eliminate the basement and the masonry garage. The basement permanently, the masonry garage for now. Can you "argue away" the basement? I managed it. For that, I had to accept a sauna, which I appreciate just as little as a basement.

My wife says building without a double garage is social housing :-(

The saying is cool, even if it is aimed at people like my husband and me.

With your wife's attitude, you will have a lot of fun building.

too rich for social housing, too poor to build XXXL

You will probably have to deal with your most expensive, because you can't just draw from the full anymore.

Yes, it was intentional.

Well, most of the houses built here in recent years have a carport + parking space, so the statement is obviously nonsense. Our parents both have a double garage, that's where the desire comes from. But that seems to me to have been a different time :-(