BÜ wants a declaration of assignment. How to avoid it?

This is not about some school-level disputes, but about a really nasty matter that gives the BU a clear advantage and us a clear disadvantage. And if one cannot contribute anything concrete from experience regarding the matter

This is mainly about a matter that you signed. And the advice here goes in the direction of not letting the relationship escalate. In return, you should check whether the contract also gives you the right to a performance bond.
As someone already wrote, at most the last sentence should be checked in terms of content or have it checked whether this can be demanded. However, I think a general contractor will not have something like this in their standard contract unless it has been reviewed on their side.

I so much wish that it were just a kind of security on the part of the BU, as you all write. However, when you enter the term Abtretungserklärung in Google, there are few pleasant texts/articles about it, with a very clear appeal – not to engage in such a risk scenario. Therefore, I also have legitimate concerns about what this can/will lead to. As many of you have also advised, I will seek legal advice on the one hand and a conversation with the GU on the other.

If you enter assignment declaration in Google, there are few pleasant texts / articles about it

However, this mostly concerns assignment declarations from the outset. Therefore, it cannot be 100% reproduced for your situation.
Your general contractor obviously included the clause only for cases in which payment default has occurred.
Furthermore, advice like "one should not sign such things" is no longer helpful to you, as it is already too late for that.

Furthermore, advice like "one shouldn't sign something like that" is no longer helpful to you, since it is already too late for that.

But it is helpful to other users who come across this topic and have not yet signed their contract.

As many of you have also advised, I will on one hand seek legal advice

It can, of course, incur costs and the statement ... everything is legitimate.

Once again – and this is not meant as an accusation or anything similar – you had a payment default. Your contract contains a clause to protect the contractor, which makes him independent of your willingness to pay so that he can manage his business securely. Especially in the currently overheated real estate markets, this is commercially sound and sensible. Afterwards, there were still disagreements, in which you suggested here that you wanted to burden the contractor with the costs of the new approval procedure after there were delays due to an unapproved planning. You had also written at the time that the time pressure was also due to your personal situation. Afterwards there were further disagreements about the soil survey, where you also expressed here that ill intent might be behind it. That is not the behavior of a customer for whom one should overlook a payment default. You have an interest in being suspicious, but so does the contractor, because ultimately it is about the existence of his company.

It is completely normal for a contractor to exhaust his legal options – to protect himself and the construction projects of other customers from payment defaults.

Legal advice is already sensible just to make it transparent for you how the claim should be classified. I do not see an initial legal consultation as a bad investment, but as expert knowledge that one cannot obtain otherwise. Especially not in forums. And possibly there is a middle way that does not completely take away the only means of pressure a builder has.

I only know the other side and for a very sensitive project we demanded a high guarantee so that in case of failure we would not be left with the repair costs if the executing company goes bankrupt. That was part of the normal contract and was not agreed upon out of distrust. It even helps for further good cooperation if you know you will not completely fall flat on your face when it gets tricky.

I so much wish that it was just a kind of security from the BU side, as you all write. However, when you enter the term Abtretungserklärung in Google, there are few encouraging texts/articles about it, with a very clear appeal – not to get involved in such a risk scenario. Therefore, I also have justified concerns about what this can/will lead to. As many of you have also advised, I will seek legal advice on the one hand and a conversation with the GU on the other.

Once again a very clear question to :

What are you supposed to assign to whom?

A guarantee has nothing to do with an assignment!