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

Lawyers also have an interest, namely to earn money through many correspondences and lengthy proceedings. Don't forget. A compromise with the construction company can be cheaper than a won legal dispute. Even if the lawyer advises otherwise.

Yes. I see the problem too. A lawyer only earns from the letters to the opposing party and one negotiation… the longer the process, the more expensive, meaning more time-consuming.
So if the reason is practically obvious here, he will advise and at the request of the OP write 2 letters. One month can be calculated per exchange of letters.
The contracting party will state the reasons in the first letter. The lawyer's second letter is the request to waive the clause, the second letter from the party is the refusal. And then? Then the trust relationship is so damaged that one should mutually waive the house construction.
By the way, it also must be said that the trust has been shaken by the delayed payment to the company. This is often forgotten here because the client only sees themselves and apparently considers companies as nothing but fraudsters (as can be read from the thread posts).

From your reports, I would conclude that there is still a possibility for a clean slate and a fresh start? Provided you want that? To me, it seems a bit as if you no longer really want to engage with it, even though issues that are bothering you apparently happened correctly.

For example, you could refer to the agreement at that time regarding the payment and simply express that you are surprised that the guarantee is now required? And also with other issues, you can openly communicate what confuses you or what you need to feel better.

From your reports, I would conclude that there is still a possibility for a clean slate and a new beginning? Provided you want that? To me, it seems a bit as if you no longer really want to engage in it, even though topics that concern you apparently went correctly.

You could, for example, refer to the agreement at the time regarding the payment and simply express that you wonder why the guarantee is now required? And with other issues, you can also communicate openly what confuses you or what you need to feel better.

A fresh start with another construction company is out of the question. It is certainly our goal and aspiration to carry through our project with the existing construction company and to complete the house without further/future problems. We can and will initiate the conversation. Still wanted to have a Plan B, what possibilities we have if the managing director does not cooperate/blocks our proposals, etc. Another problem could be that the bank does not cooperate and does not issue something like that.

It is logical that we are not looking for conflict, but want to complete our house and carry out the construction process as smoothly as possible.

So for defects, you have the possibility to withhold some amount from the first installment as far as I know.

If I were you, I would possibly sit down with the [GU] and speak openly. Also openly communicate your own mistakes and make it clear that you are unsettled by one or the other point.
Make the goal clear, to work together trustfully until the end.

So for defects, you have the option to withhold something from the first installment as far as I know.

The last paragraph in the contract clause explicitly excludes that, unless the defect is undisputed and/or legally finally determined. I guess that the last paragraph is also possibly the one that a lawyer might challenge due to disproportion.

I have not passed judgment on your payment behavior here, only given my assessment of how your distrustful behavior might affect the contractor. I also professionally deal with clients who want every little detail to be evaluated by an expert instead of accepting that some standards and measures are absolutely within the quality standards, even if the layperson does not see it that way.

Now the good gentleman, the owner of the construction company, informed us that he would like to have an assignment declaration from us. This clearly creates a disadvantage/high risk for us.

It is now the case that, contractually, it is possible for the construction company to demand this service from us.

Distrust often arises due to lack of communication. Contract partner A wants contract partner B to do something. Contract partner B does not know what is intended and therefore grows distrustful.

You write at the beginning (see quote) that the contractor wants an assignment declaration from you. Did he really say that and mean it that way? What exactly are you supposed to assign to him??

With an assignment of claim, I can transfer a claim that is due to me to a third party, e.g. I assign my claim for damages against the party at fault in an accident to my workshop, which then collects the money from the responsible party.

However, you attach an excerpt that deals with a guarantee. That is something completely different, isn't it? Are you sure the contractor even meant this?

If the terms get mixed up like this, no matter by whom, I can only recommend a clarifying conversation, both with a legal advisor and with the contractor.