There are two great key figures:
How high is your current cold and warm rent?
How high is your current savings rate?
Does that fit with a house installment of 1350€, 150€ reserves and 400€ incidental costs?
It is quite tight. Price-wise probably a good opportunity, but ultimately already too expensive for the family. 33% of the household income would just be feasible for the installment.
You have to weigh whether you want that. If the own house is a lifelong dream, then you might accept compromises in other areas (vacations, clothing, etc.).
Difficult. If the situation in the real estate market does not change, with the income you will definitely be out in the future. But is exactly this feeling (FOMO) a sensible advisor for a life investment?
I would only do it if I can complete the whole project with repayment subsidies (Baukindergeld, etc.) and fixed interest (fixed for 20 - 25 years) without inheritance.