A woman who committed adultery with her husband's consent

Hello Rabbi.

A question that interests me, and although I tried to find sources for it, I was disappointed to see that there are almost no sources to review.
A woman who committed adultery voluntarily and with the consent of her husband (as is done today in couple swapping) is this called adultery?
On the one hand, I saw that the verse in the Feast (9:1) does say, "Who is the one who is twisted and cannot be corrected, etc., who comes upon a man's wife and forbids her husband." On the other hand, the verses in Parashah Sota say, "And he brings him up above" that the thing was done without the husband's consent, under his authority, and in secret. "And he disappeared from the eyes of the woman," "And she was not caught."
I also saw that the gaon, author of the letters Moshe (Iven HaEzer, Part 4, Sign 44, Letter 6), looked into this a bit in the case of a woman who married a Gentile with her husband's consent and came up with the idea that if she did so completely by mistake, thinking that she was forced to commit adultery in order to please her husband, then perhaps it should be said that she is not forbidden to him.

And I saw that indeed there is a division in cases of adultery, one that is a sin against heaven, as in the parsha of the holy ones, "And a man who commits adultery with another man's wife, and a man who commits adultery with his neighbor's wife, both the adulterer and the adulteress shall be put to death," which does not depend on the husband's misconduct, but rather on the sin itself. On the other hand, the very "prohibition" that is prohibited on the husband depends on whether "he commits an offense" and if the matter was with his consent, there is no misconduct here and he is not prohibited on him.

And the very prohibition that is forbidden to the husband is not taught explicitly, but rather a doctrine of "as is forbidden to the husband, so is it forbidden to the adulterer." But is it forbidden simply because it is forbidden or because in the most ordinary situation the husband would divorce such a woman when he discovered that she had committed adultery, but in such a case, if he wanted to, what is the ruling?

And one should also note from the Tosafot Zebachim (2:) that a woman is not eligible for divorce – "and even if she has committed adultery under her husband" and it is mentioned that he can keep her and not divorce her, as long as she does not use us.

I would love to know more about this.