Financing via KFW 55 or still from the bank?

Yes, I see it that way too, but just don't really know how to proceed... I would certainly set aside the "excess" money and immediately as much as possible

Where is the uncertainty in the approach?

Well, you first have to find out where the additional cost for kfw55 lies. Can your construction company roughly answer that for you? Or is it already fulfilled with the current insulation and technology?

Then find a bank that does it without another loan. In my case, Raiffeisen banks and savings banks would be interested. Then see if you can provide other securities besides an entry in the land register (e.g. funds in a fixed deposit). Because, an entry in the land register costs money.

And either in parallel with the bank or beforehand find an energy consultant who does it at a reasonable price. The range of offers for me was a factor of 2. And see if they have to calculate many thermal bridge details etc., that also costs extra