I didn’t understand. I read that Nefesh HaChayim in the past (following your recommendation), and throughout the chapters he talks about some kind of mystical connection, and when a person speaks words of Torah it is as if the Holy One, blessed be He, is speaking. That doesn’t seem to me like a rational explanation; perhaps it is also true according to Kabbalah. In any case, I’m asking about the second possibility I presented—what do you think of it?

I already wrote my opinion. What’s the point of repeating it?

“Moreover, I said to come with the scroll of the book written about the greatness of the obligation of engaging in Torah… for even at that very time when a person engages in Torah down here, every word that comes out of his mouth—those very words also come forth, כביכול, from His blessed mouth at that very same moment… for the supernal root of the holy Torah is in the highest of the worlds, called the worlds of the Infinite, the secret of the hidden garment…” (Nefesh HaChayim, Gate 4). Do you see a rational explanation here? I certainly haven’t merited to. I’d be happy if you could help.
In addition, “Even if he is occupied with aggadic passages that have no practical implication for any law, he is still attached to the speech of the Holy One, blessed be He.” According to the rational explanation, this is really not understandable, and if I remember correctly I also saw that you wrote that there is no point in studying aggadic literature.

As is well known, the definition of a rational explanation is: my explanation, as opposed to other explanations.
I don’t know what kind of explanation you’re expecting. He claims that the study itself is attachment to God’s will and therefore attachment to Him Himself. Is that not rational enough for you? Then no.
Indeed, in my opinion there is no study-value in learning aggadic literature, but to the best of my understanding there is also no intrinsic metaphysical value to it either (because I do not accept that the aggadot are the word of God).

There are also ethical teachings and encouragement in the aggadot to keep the Torah. Is that Torah study in the personal sense?

In my opinion, such a thing is not study at all. Study is the acquisition of knowledge. Character refinement and keeping the Torah are not study; therefore they are also not Torah study.