Regarding Kfw: 2.65% is the home ownership program. BUT if you build, for example, a Kfw70 house, there is the energy efficiency program at 1.41%. If not, that option is eliminated.
Regarding the building savings contract: I simply see a high risk for you in the annual approx. 8,000 EUR lump sum payment into the building savings contract. If that doesn’t work, the building savings contract will not be eligible for allocation after 10 years and you will be stuck with the full 177,000 EUR at interest rate risk.
This is always difficult to assess from a distance, but I could imagine that you would be better off with, for example, a building savings contract for 50% of the amount (e.g. 80,000 EUR building savings sum). If you really have the 8,000 EUR left over each year, put 4,000 EUR into the building savings contract and 4,000 EUR as a special repayment on the loan. That gives you a much greater savings effect!