The planner does not perform any calculations according to DIN 276

Wow- thank you so much for this great - enlightening answer!
This not only does good to the soul / at times I doubted my sanity, at the same time it gives me strength to now once again formulate a letter in her direction.

It is simply difficult for me in one place or another not to react emotionally, because these partly glaring mistakes - and above all her reaction to them simply make one powerless.
In her last email - referring to her final invoice - she wrote that she was considering coming to us with the police, because she was afraid it would end in shouting if she wanted her money.

I found no answer to this, as this is naturally unbelievably ridiculous on her part - because even with a legitimate claim, that would hardly be a businesslike way to demand payment of an invoice - so far I only knew of the reminder as a payment request...
which at the latest the police would probably have told her (civil law, jurisdiction, etc.)

The whole situation has really already led me to a kind of powerlessness, because I simply cannot grasp what all has happened there.

When I look into the hoai, I really get dizzy - she explicitly bills according to it and simply did not provide so many services.
What makes me even more speechless is her consistent ignoring of our requests - already during the construction phase and now ultimately the statement that she does not have to provide these services - after all, the house is finished.

Is she an architect or not?
If she is not an architect, maybe she is not allowed or does not have to provide the service.
If I read it correctly, specialist planners only handle partial tasks (e.g. structural engineer).
They also bill according to HOAI.

Is there a contract with the architect, covering which service phases?

Yes, of course there is.
An "architect contract" that commissions her with all service phases from 1 to 9. This contract refers to the HOAI, as does her invoice, as well as an attachment. I will look for the contract at my father's place tomorrow - then I can report exactly.

: What do you really want to achieve? It can hardly be about a retroactively filled estimate.

In her last email – referring to her final invoice – she wrote that she was considering coming to us with the police because she was afraid it would end in yelling if she wanted her money.

That’s just noise. The police will just show her the finger beforehand anyway. She should provide verifiable proof of her services – 11ant has written enough about it and I had already asked whether she was really an architect.

since this is obviously unbelievably ridiculous on her part

Of course. But there may be people who let themselves be intimidated by this.

so far I only knew the reminder as a payment request…

It was no different in the past and won’t be different in the future. Next a payment order and then going to court.
Moscow debt collection is also just another payment request, but already well in the gray zone of legality.

When I look into the HOAI, I really get dizzy – she explicitly bills according to it and simply hasn’t provided so many services.
What makes me even more speechless is her consistent ignoring of our requests – already during the construction phase and now finally the statement that she doesn’t have to provide these services – the house is finished after all.

Sometimes “normal” talking with each other is not enough. Then communication has to go through third parties.

A nice example from my circle of acquaintances. I have a friend who lives cheaply but simply. The landlord, an older gentleman, is only interested in money. He saves on property management. But he also saves on expertise for the utility bill (and also for heat cost allocators – there are heat quantity meters on the supply lines to the apartments which should have been replaced nearly 40 years ago and haven’t worked for ages. Therefore the heating cost billing is done on the basis of cbm gas consumption for individual apartments in a central heating system…). Which has still worked out quite well in the past.
Now in the last two years there have been defects in the apartment and claims against my friend of about €700 for 2022 and just recently about €1,600 for 2023. There has been no response to the objection to the 2022 utility bill so far. The defects have not been fixed so far. Communication is a disaster – at best a “leave me alone with this, otherwise there will be a rent increase.”
Now finally she let herself be persuaded by me to have a letter drawn up by the tenants’ association (by a female lawyer). From receipt of the letter to contact for a discussion about a “deal” took a good 6–8 hours. What a difference it makes when mail comes from a legal assistant and the defects in the utility bill are listed and a rent reduction due to the defects in the apartment is threatened. Let’s see what the discussion brings in the next few days.

Of course I do not want to pay the 6,000 euros she demanded from the final invoice (total amount 67,000 euros) at first, because I believe that even without clarification about the warranty (there are already significant defects here besides all the trouble – including the brown crazy ant…) and the resolution with the roofer, the construction is not yet finished.

Don’t get me wrong – my father really paid every invoice within minutes – and also wants to reach an agreement with the roofer, but this is not my father’s fault, since the planner arranged all the appointments with the craftsmen. Why does he now have to pay 12,000 euros for scaffolding that wasn’t used – not even by the roofer who set it up?!

To be honest, I am sure we are even in the area of damages here – so it is hard for me to pay her any more, especially since no cost determination has been made yet / and she simply claims “it’s just a bit expensive? But it turned out nice” and sends us cheeky messages like “look what a house from 1700 renovated 30 years ago still sells for.”

That is no basis at all.

What if she isn’t an architect at all – but only a “specialist planner,” can one then conclude such a contract for all service phases – according to HOAI including appendices? Is everyone allowed to do that?

whether it would be worth it for me not to pay 18k to the roofer and [arschitektin] and to draw a line under it.

I believe the price increases due to incompetence and naivety have led to the immense additional costs