With this whole setup, so many alarm bells are ringing for me, I don’t even know where to start.
Are you sure that you will get the KFW 300 loan? That can only work if you haven’t been receiving this salary for very long. This house price including QNG and foundation slab from Viebrockhaus can never, ever be correct. Be sure to check the construction service description carefully. What is included and what is not? And then please make an Excel sheet where you try to determine all the costs. I can recommend the template from Fertighausexperten for that.
We have a similar household income (even somewhat higher), only 2 children, only vacation in Germany in holiday apartments, and after deducting the expected additional costs for the house, I have come to the conclusion that we can “only” afford a rate of €2600 with a clear conscience. You should definitely calculate this thoroughly again and better be pessimistic than optimistic.