Good morning
so financing:
a standalone KfW loan for the new property (€100,000) with bridge financing on the old property will probably not be given by any bank here (because they have more work to do (valuing 2 properties) and will hardly earn anything in the long term (10-15 years) on the €100,000)
therefore this option is off the table.
banks can provide bridge financing if they provide a larger, long-term loan on the new house (at least €100,000 without KfW)
therefore, I would choose the "grant variant" at KfW, without a loan. This means the money goes into your account instead of being a repayment subsidy at the bank.
to keep things uncomplicated here, something like this would be "recommended"
you buy the house for €275,000
€100,000 comes from financing at the bank
€175,000 is bridge financing (until the property in Bavaria is sold)
the incidental costs are paid out of pocket. (€25,000)
(equity investment: €25,000)
you then pay for the modernization completely out of pocket, or you do that first so it is ready to move in.
other things, such as outdoor facilities, can be done gradually, especially after you have sold the property in Bavaria and the money has come in.
that means depending on modernization costs, you might initially invest €125,000 of equity... and the rest when you have the money from Bavaria in your account.