Thank you very much for all the helpful feedback!
I tend to feel encouraged to switch from tax class IV to tax class V, which reduces my net income, despite the intended house purchase as a higher earner, so that my wife (in the then chosen tax class III) can receive more parental allowance.
Since we only got married this year, we are exceptionally able to make the tax class change retroactively to the month of marriage. This means that the period I have to spend next year in tax class V will not be too long, and the net deficit regarding this year’s period can at least be balanced out by mid-next year with the 2020 tax return. Immediately at or after the birth, I will then switch to tax class III, which increases my net income again.
What seems decisive to us is especially the fact that we have not found a concrete purchase object yet and the further search (without us wanting it) may possibly continue well beyond the birth.
If we find something before the birth and thus during my time in tax class V, I will explain to the bank that the net income is only temporarily reduced and hope for their understanding / benevolent assessment of my creditworthiness. After all, the temporary switch means that, (albeit with a delay) we will ultimately have more money overall than without the change due to the increased parental allowance.
Once again, many thanks to everyone for the support in our decision-making!