Is serious construction financing possible?

They help and mediate - the documents that then need to be filled out are from the KFW and are forwarded by the bank.

These should also be prepared by the bank.

Do banks also help with the KFW funding programs or do I have to handle that independently?

It depends on the funding programs you would like to use. It’s certainly not a bad idea to simply browse the KfW website.
For example, if you are building with 153, you will need an expert anyway.
Ultimately, the funding programs are processed through your house bank. So contact them early.