New KFW funding possible with old work contract?

So it indeed seems that with an existing contract for work the new subsidy can no longer be applied for. The reason is a change in the application conditions. Until 30.06.2021, the funding application could also be submitted after the conclusion of the contract for work, but had to be submitted before the start of construction work. Now the cut-off date is the signing of the contract for work. But that is still not enough, because as far as I have found out, the KFW confirmation of receipt must even be awaited before signing.

I feel poorly advised and misled by the construction company in this matter. At the time of signing the contract in February 2021, the construction company must have been aware of both their excessive order volume (which I could not assess) and the impending rise in material costs (which I was aware of).

Conclusion:
Even if I take legal action against the poor advice or the construction delay and thus the price increase, I will no longer qualify for KFW funding.
I would therefore be forced to agree to the new, more expensive contract in order to benefit from the €26,250 subsidy. What do you think?
Maybe I can have the price adjustment clause removed in the new contract or get reimbursed for an additional service.

A different question. I have now submitted the application for the grant (kfW 55 -> €18,000) and received approval. Now it says something about identification. How does this take place? Unfortunately, I couldn't find anything about this. Or does it only happen shortly before the payment?