Hello Clairiana,
well, you have already covered or considered all eventualities. From my observation, unfortunately, a lot has happened with house prices in the last 3-4 years. Because of the low interest rates, a lot is being built, high demand with a stable supply situation drives prices. And land prices have also developed dramatically in recent years. Where we currently live, 5 years ago the sqm in a new development area cost about 140 euros. Currently, another new development area is being planned. They are currently expecting sqm prices of about 220-250 euros!
Well, with the 600,000 euros you are not so far off with the "cheap" option. Since flooring, painting, garage, and garden are considered separately, the 50,000 € additional costs seem very generous. Of course, it also depends on what you include here, what the soil conditions are, etc.
I would now simply talk to a few providers (e.g., the mentioned construction company) and see what offers come in. Then you will get a better feeling for the prices and costs of your dream. At the same time, already start addressing the topic of financing.
Regarding your last question: We are currently in the middle of the construction phase in northern Lower Saxony (between Hamburg and HB). A "normal" single-family house with 149 sqm living space. It will be finished in August, and we are currently working in the garden every free minute ;)
Best regards
Michael