Procedure for buying and renovating a house

No, you misunderstood, you won't find a bank that will give you "only" the [KFW loan].

I meant first buying the house (taking out only the 145k minus equity - no buffer!). It is important that it is a variable interest loan. This allows you to repay the loan in full at any time without a prepayment penalty (to restructure). That costs a bit more interest, but it is only for a few months.

Then pull out, plan, get offers and with the finished plan and corresponding offers see if the [KFW funding] in the loan variant makes sense/works for you.
Both aforementioned programs exist in the form of a loan or as a grant.
Then show up with the required amount at the loan broker, possibly still check 1-2 local banks yourself and finally accept the best overall offer.

The advantage is that you have enough time to plan everything carefully and calculate the corresponding funds, and of course, ideally, all parties are already ready to go.
On top of that, you take some pressure off the matter because you don't have to repay the variable loan at all or only very slightly, and the monthly burden is correspondingly low. And of course, you don’t have to panic and take out the next best loan based on a cost estimate "from the internet" because the seller is pushing ;-)

I first meant buying the house (only taking out the 145k minus equity - no buffer!). It is important that it is a variable interest loan. This allows you to repay the loan in full at any time without prepayment penalties (to refinance). This costs a bit more interest, but that is only for a few months.

I would skip the hassle with the variable loan and directly take out a generous standard annuity loan. You can also apply for KFW subsidies later after you are in the house. The only important thing is that the application is submitted before the start of the construction measure (and the bank agrees).

Depending on the federal state, other funding programs may be applicable. For NRW, I can recommend NRW.Bank.building renovation. That is 75k at 1.65% interest fixed for 20 years (full repayment). I find that much more attractive than KFW since no special requirements have to be met. Disadvantage: online banks and intermediaries rarely offer this. So go to regional house banks.

The combination of e.g. NRW and KFW is only rarely possible since not all renovation measures are eligible for funding.

I see you are in Niedersachsen. Take a look at "Energetische Modernisierung von Wohneigentum" from the NBank. Maybe there are other options as well.