There is no accounting problem since you are not entitled to input tax deduction. Therefore, §14 USTG, which describes the mandatory components of the invoice, does not apply to you. And even there, the only issue would be the date of service, and you could indicate the expected date of service.
I believe we don’t need to discuss this any further at this point. You signed the contract as it is, so you are obliged to comply. No one can tell you how the company will react if the money, for example, arrives in the account 2 days later. In my opinion, according to the Building Code, the wording is even lawful; regarding VOB, I cannot say anything.
For this, you would need advice from a lawyer and could also ask about the consequences of deviating from the contract. Such a letter from a lawyer or a short phone call can sometimes work wonders and costs peanuts compared to losing a whole installment in the event of the construction company's insolvency.
If you have a construction supervisor, they could also support you again because, in my opinion, the money should only be transferred after acceptance of the individual trades.
Alternatively, I would try to negotiate a compromise with the company again. For example, 50% of the money is in their account on the day of delivery, and the rest is paid immediately after acceptance/determination of actual delivery.
Here it would be necessary to look at how high the individual installments are and whether 50% of the installment could be borne if necessary.
But it also depends somewhat on the payment plan, so you don’t end up advancing too far already, whether you possibly have a completion guarantee, etc.
If you post the complete payment plan, Bauexperte might be able to review it again.