HOAI represents a maximum fee. Architects may voluntarily charge less, but not all do.
You can inquire about the costs for the building permit at your responsible building authority.
In our case, the costs for the building permit were €480.
If you fully comply with the development plan, there is even the possibility of obtaining a building permit through the simplified procedure (this would have cost us €50).
You can also submit so-called preliminary building requests, which are cheaper than a proper building application but still provide a binding answer from the building authority on whether, for example, deviations from the development plan will be approved. With this, you could then potentially enter the simplified procedure (at least that's what I was told back then).
Ultimately, a phone call to the building authority about the various options also helps. They don’t bite there.