So with your salary, the rate is definitely manageable. For comparison: Our rate is about €1,000 higher (here the price per sqm is €500 and the house is bigger). Before the birth of our first child, we also had just under €7,000 available monthly together. My wife took one year of parental leave, since then she works 30 hours a week and our child is with the daycare provider and two afternoons a week with the grandparents.
Current situation:
Income: €7,200 (incl. [Kindergeld] and I have had a salary increase)
Housing costs: €3,000 (house rate and all costs related to living)
Partner’s car: €500 all in (I have a company car)
Daycare costs: €550 (I hope that is cheaper for you)
Vacation savings: €350
Child expenses: €400
Groceries/adult food: €800
Clothing, leisure, insurance, etc.: €400
Remaining: €1,200
We are saving the remainder for now. A second child is planned, so one more year with lower income will have to be bridged and then higher expenses will arise. Nevertheless, there is still enough buffer for special repayments, for reserves (repairs and renovations), and also in case the follow-up financing would become more expensive at the end of the fixed interest period.
In other words: You are doing pretty well financially and the housing costs are in a very good relation to your overall situation.