It's a bit confusing... I'll try to sort it out:
1. Contractual relationship
In Germany, a contract does not require a signature! Contracts can also be concluded orally or arise through "implied conduct." Whether justified or not, the architect will probably rely on that - and likely succeed! If I were you, I would assume that a contract has been concluded.
2. HOAI
HOAI is a phase model in which the construction project is continuously refined from phase to phase. The purpose of the phases is above all to identify potential obstacles in time (i.e., in early phases). The impossibility of being able to build at all should have been recognized and demonstrated by a technically and locally knowledgeable architect at an early stage. According to my—layman's—understanding, billing should only be done up to that phase at most.
If an oral contract exists, standard HOAI applies—without extras, etc. In this sense, the invoice should also be itemized, which can be easily checked. In particular, this check must include up to which phase was billed and based on which construction volumes. I can hardly imagine €18K for Phase I and possibly parts of II for an extension.
3. Partial services
Assuming a contractual relationship exists (see 1.) and HOAI applies to it (see 2.), the "partial service tables according to Siemon" help determine the correct fee—because quite obviously essential parts were not delivered!
4. Surveyor
I cannot judge whether the necessity of a survey can be derived for the architect/surveyor from 1. and 2. It seems that even without a survey, it should have been clear that an extension is not approvable.
5. Lawyer
There are specialized lawyers for architects' law—who quickly clarify such a case. Regular lawyers are usually overwhelmed by it.
Good luck!