There’s this claim that if I’d agree to be killed and have someone created immediately who is exactly like me (including everything), that proves there’s no soul, and that my uniqueness lies in paradigms and such, not in some higher thing.
I would apparently agree to something like that—does that really prove anything?

Regarding dualism itself, I think you can read a very nice treatment by the Rabbi in connection with his book on free choice.
It may not be a description of the essence of the soul, but there is a kind of indirect proof there for its existence. Strange that he didn’t refer you to that, if that’s what you’re looking for.

Rabbi Steinsaltz has a book called “Soul,” and it deals with its manifestations in the world—or better, in the human being. It isn’t a book that comes to prove its existence; it assumes it from the outset. In my opinion, the book is based on modern interpretations of Sha’ar HaGilgulim and probably other books from the field of Kabbalah. Even though the book doesn’t deal with proofs of its existence, only with its manifestations, it’s still worth reading. It gives an opening for approaching the subject. As is well known, Rabbi Steinsaltz was a wise, educated, critical person, with a restrained romanticism regarding matters of Judaism.

I’m not looking for a proof—I first want to understand what it is????

Hello Yehuda,
I don’t know whether this will give you an answer, but I recommend watching the following video by Rabbi Lundin (about 4 minutes).

https://youtu.be/_TtrdVdnPps

By the way, from what I understand, the Rabbi Michi’s site (and Michi himself) is packed with monotheists, and people who think that we and God are two completely separate things, so take into account that the video may not entirely fit Michi’s approach.