Responsibility of the architect in case of KfW interest and further matters

We received the certificates, the invoice from the structural engineer, and the corrected invoice from the architect on Friday. There are also two pages included, which we do not know whether they are from the architect or the structural engineer. There are also other items listed that the excavation is supposed to come from (see picture). However, the area of the garage has NOT yet been excavated.

Does anyone perhaps know overviews for such exams?

Yes. The cost estimate from your architect according to DIN 276 from HOAI LPH 4 should serve as a guideline here.

Unfortunately, that doesn't help if the performance description/the bill of quantities is rubbish, and the underlying quantities are faulty/guessed. For example, in excavation and disposal, I am missing the installation class/assignment value (Z0-Z2). Just depositing Z2 alone costs >50€/t. Plus landfill acceptance fees, handling, and sampling, that already adds up to a nice amount per ton. The risk of having to dispose of Z2 material at one's own expense, due to unclear specifications, is borne by few/nobody.

tl;dr: Construction costs in single awarding stand and fall with the quality of the tender documents. If the bill of quantities is poor/unclear, high costs arise in individual items, additional costs in quantity increases, and claims for additional payments that are already pre-formulated in the drawer before the order confirmation.

Do you have any tips so that we don't end up getting burned like this again? :-(

Yes. The cost estimate from your architect according to DIN 276 from HOAI LPH 4 should serve as a guideline here.

Unfortunately, we still don't have it, but we have requested it. Today, an email arrived: "Mr. xy [former architect] and I are currently working on a current cost estimate."

This clearly shows a breach of duty – he still isn't planning a cost estimate.

I have one more idea, maybe someone can correct me: Is the structural engineer commissioned according to VOB? Was his offer based on the specified quantities? Billing of the actual quantities at the offered unit price?

Then a) his performed service must also be paid (expensive for the TE). But the structural engineer would have had the obligation to immediately report quantity increases as soon as they were recognized. The originally offered quantities may then be billed at the offered unit price, the additional quantities must be recalculated at your request and this calculation must also be proven. Maybe a few euros can still be recovered from this.

The cost estimate from your architect according to DIN 276 from HOAI LPH 4 should serve here as a guideline.

The cost estimate logically only exists at the time of awarding the contract (service phase 7) and it only reflects what the companies included in the bill of quantities, so it does not prevent additional charges and/or incorrectly planned quantities.

At this point in time, the only thing you could demand is the cost calculation (service phase 3). But whether it is actually more substantial with this architect than the estimate, I doubt.

However, I stick to my point: in the end, it costs what it costs. You can only save on "non-essential" items such as, for example, the ETICS or the garage or by "reducing" the execution quality.
Of course, it is desirable to know beforehand where the journey is going, but in your case, the train has already left the station – the loan contract signed, construction started. So why waste much energy on how it could/should have been?