Unpredictability of construction costs - Will the project fail because of it?

Our planning would be more than sufficient to receive the funding. Our energy consultant was right after all.

This info is for all self-proclaimed energy experts here ;)

Of course, KfW doesn't care how tall the room is. But further up in the thread it clearly stated that KfW only funds living space. However, you don't have living space because it does not meet the applicable standards.
Try, but don't be disappointed if it then fails.

Is it exclusively about the funding, or is it actually supposed to be rented out?

I think it will go through, as long as the KfW does not order a more detailed examination. It's pure gambling.
Addendum: Which federal state? There are many exceptions, including in the basement and with small residential units depending on the federal state.

We can describe it like this: Definition of a granny flat: “What defines a granny flat today is legally clearly defined. The crucial point is that it is a self-contained residential unit within a residential building. A separate entrance is not strictly necessary. Sharing a hallway or stairwell is also permitted. However, sharing a kitchen or bathroom is not allowed. Because a granny flat must provide its residents the possibility to run an independent household. Completely independent from the other rooms in the house.” Source: Schwäbisch Hall.

But this is more interesting, and it comes to the point further below: “Regarding room height, the state building codes give very specific requirements about what applies in your federal state. For example, a basement used as living space must meet a minimum room height. 2.30 meters is considered the lower limit, but 2.40 meters or 2.50 meters room height would be better.” “Check what applies in your federal state. If your basement does not meet this basic requirement, it can become a knockout criterion, because the room height cannot be corrected afterward.” Etc. Source: mein Eigenheim

The KfW bank assumes that everything is correct, since they only support granny flats. If you do not legally build a granny flat, you do not need to submit an application.

In Bavaria, that is 2.40 clear room height

In Bavaria, that is 2.40 clear room height

As has already been correctly stated here in this thread, this does not apply to building classes 1 and 2. This post was created in a 2.25 m basement living space.

As already correctly stated here in this thread, this does not apply to building classes 1 and 2.

This post was made in a 2.25 m basement living space.

Stupid question, since I just googled the building classes: 7m maximum height can be tight for, for example, a city villa, right?

How is it measured when building on a slope? OK ground floor level?