Basically, the rate looks feasible at first glance and quite generally (30% of the net income), and I also believe you regarding the savings over the past months. Regardless of the construction costs, it should be said that kitchen, furniture, etc. have nothing to do with the construction costs ;)
Assuming 420k, you would probably manage with the targeted rate of €1300, additional monthly costs for the house should be estimated at €350-500. If we assume that, then we would be at "from €1700" per month for the house. Currently, you pay a good €700 in contrast, which means that of the €1500 savings rate, only €500 remain in the future. From that, you might eventually need to buy a new car (a car is currently set at €0 monthly), pay for its repairs (these are also set at €0 for both cars) and cover any other unplanned expenses. Banks generally calculate an average of €500-600 per month all in for a car, which is not unrealistic for mid-aged, mid-/Golf class vehicles for an average work commute.
I don’t know whether additional income is already included in the consideration of your current savings rate? Balance at the end of the month in the account or really determined individually.
If parental leave is coming up, there is 65% of net income, which in your wife’s case (I assume she is more likely to take parental leave ;) ) would be €1300 instead of €2000 per month, and you would be in a monthly deficit without special effects, so either savings or other sources would be necessary. Additionally, a child also costs money, and the roughly €200 child benefit is often not enough; for example, a daycare provider at €300-500 per month is more the norm than the exception. Can your wife go back to work full-time afterward or only part-time?
These questions are best worked through together in the evening and then honestly reviewed and decided upon, possibly developing ideas; it seems there are reserves that were not mentioned here.