A few notes. Based on the current consumption level, a 2500 installment is actually problematic. It was correctly noted that mobility costs in more rural areas with a child are at least questionable (for example, if you are a committed eco-friendly person and can walk to work, etc.). It was also correctly noted that costs increase noticeably with a child, not least the intended external care in the nursery age is not adequately considered (otherwise 400 euros won't be enough). I also don’t know if the initial equipment is really a big point. You can actually get by with 1000 euros. Of course, this does not apply if you buy everything brand new. Then 400 euros per child are even less sufficient. It was also rightfully and critically noted that the insurance sum is low. I am not a fan of insurances, but with a child, better coverage would certainly be appropriate.
Summary: with your current lifestyle, even a 2000 installment is tight. But: of course, with the stated incomes, you could also manage 2500 (but then please new construction and no existing property with incalculable risks), but you have to adjust yourselves. Some do that automatically with a child. Some have to fly 4 hours on vacation even with a baby. From a distance, you cannot judge that; you have to know that for yourselves.
Regarding working hours: as a thread starter, I would not react so snappishly to critical remarks here. Of course, you can work almost full-time twice with one child. But then you have to live with the fact that aside from the child, you have no time for other hobbies + social life. That naturally improves with the child's age, but I can't understand why one unnecessarily pushes oneself to the limit especially at a young age. A baby is already very demanding with just one full-time job and one parental leave.
In view of your current situation and the fact that you don’t want to be more than 3 people anymore (realistic given the age), the following advice: 80m2 is enough to spend the child’s first 3 years in the current apartment. With kindergarten, everything is also better plannable, and you can better assess how much you can work (certainly more than in the first 3 years) and to what extent you have adapted your consumption-oriented lifestyle. Then it will probably already be biologically certain that it will remain with one child and you can exactly estimate how much living space you need. Then do a balance sheet and buy only as much as is financially possible in the end. Be it an apartment or actually a small house. That’s all you need for 3 people. Currently, that would probably just be affordable for you in a rural area (but I’m not familiar with NRW) (2.5k installment roughly corresponds to a 500k loan at 2% repayment + 200k equity).
Additional: just because you are engineers, I wouldn’t dare to take on a renovation or even a refurbishment. You don’t need theorists for that but practitioners (craftsmen). That you can think through all renovations well doesn’t help much if others have to carry out your planning expensively. If you don’t have other capacities in the family for that, I would rather refrain and go for new construction. With 3 people, you don’t need that much space and if you buy at nearly 40, you simply have more of it. Not to forget that with every hour more work on even the simplest own services, you slide into a time bottleneck.