It doesn’t seem to me that I understood why a perfect being cannot legislate evil (and if so, what defines the Creator of the world as such at all), and why, if moral duty does not exist, the fact that He legislates evil causes Him to lose authority. More generally, if indeed the first link in your normative assumptions is that the validity of the moral law derives from the lawgiver (since it seems that you reject godless moral realism), why should there be an assumption of a connection between the duty to obey Him and the conformity of the content of the command to some world of ideas or another (even if you say that its very existence is external to the lawgiver because the definition of good and evil is true in every possible world)?

A perfect being is supposed to be good. Actually, one might perhaps say that He is supposed to “choose” the good. But this is a compatibilist “choice” (that is, one that could not have been otherwise in light of the chooser’s nature).
If He legislates evil, then part of His authority falls away, because part of it is based on His being good (beyond His being the Creator).
But as stated, this is a hypothetical discussion, because we live in a world in which there is valid morality and a good Creator (on my assumption), and it is doubtful how far one can discuss another world from within that framework.

If His authority is based on His being good, how is this different from the usual position of moral realism, aside from the fact that there is another entity that receives the validity of morality (but is also bound by it as moral facts)?

That entity is not bound by it. Its nature leads to it. In the language of the later authorities, “the nature of the good is to do good.” Once He is bound by it, He commands us, and that obligates us as well. I argued in Column 457 that morality is true in the same way mathematics or logic are true. There is no possibility of a different good. But the question of whether to do the good is a different question. That is, the claim that the good is not merely a neutral fact but also something that obligates action (from what is, to what ought to be). But the obligation to do good (as opposed to the definition of the good) requires authority. The Holy One, blessed be He, who is perfect and all-knowing and acts rightly by His very nature, is bound to morality, and we are obligated by force of His command.
One should remember that the Holy One, blessed be He, is also bound by logic and mathematics. These are necessary relations by their very nature, and therefore there is no subordination here in the usual sense of being subordinate to a law or to someone else. In our case, authority is required in order to obligate.

If mathematics and logic were necessary, there would not be an abundance of logical systems and mathematical theories built on different and even contradictory axiomatic systems. Can something be “necessary by its very nature” even though there are alternatives, and useful ones at that? And moreover, that the Holy One, blessed be He, is “subject” to it in some unique way because of that? That doesn’t work when the very talk about “logic” with a definite article is itself a huge problem, as anyone who took an introductory course in the philosophy of logic would know.

This is nonsense. You should review the course. When people speak of different logics, this is not a substitute for classical logic. Łukasiewicz’s three-valued logic, for example, is itself discussed through ordinary binary logic.
As for mathematical axioms, that is already a real misunderstanding. Every set of axioms in geometry represents a different reality (space). For a given space, there is only one correct geometry. Beyond that, mathematics is not the axioms but what is derived from them. The logical rules of derivation are uniform and agreed upon. When other systems are presented, they are not a substitute for that system but a conceptual framework for a certain context within it.
It’s hard to elaborate here, although this is a very common mistake.

If the move from the desirable to the actual does not happen without the legislating entity, how can one say that if He chooses evil this undermines His authority?

I don’t see the connection. I explained that our obligation derives from His command. But in His case, moral commitment is not a duty but a result of His nature. If His nature were different (evil, imperfect), His authority would be undermined.

Michi, where did you elaborate on this “nonsense”?

I don’t remember having elaborated on it in one specific place. I commented on it in several places.
For example, in my article “What Is ‘Halut’?”, in the article on contradictions and quantum theory, and in columns and responsa about the nature of the “laws” of logic (which are not laws like the laws of physics or the laws of the state), and therefore God Himself is subject to them.