I don't think bio sex is a social construct. She doesn't say that in that article either, I don't think. If bio sex is a social construct, then so is everything else, and we can stop referring to anything as a social construct and just refer to things as things.
I think that social construct should only refer to things that have no existence outside of the meaning put on them by people (money), or the mechanism by which we understand things (we understand bio sex, not a social construct, through the mechanism of a social construct, gender).
So when people say that bio sex is a binary, or a spectrum, or anything else, what they mean by those things and how they perceive those things is socially constructed, but bio sex remains a material reality.
In that quote, Butler says that there can be a sense of sex used for assignment. and another sense used to reject that assignment. She is saying that in the context of trans issues, but the same can also be said for females. Our ideas about the female body may be somewhat different to those intended by the system of assignment or by what is known by science.
Science, within my lifetime, has found out new information about what the clitoris does, due to new technological developments (or at least the new use of them). But the clitoris was doing the same thing before science proclaimed it to be happening.
Feminism has its own perspective on the female body, a second sense, just as Butler is saying. The transgenderist approach also does. But for some reason, many transgenderists attack feminists as if they are the medical/legal establishment and the thing that is being resisted, when we are simply a different form of resistance (just one that is incompatible with theirs).
There has to be a distinction made between resisting the way knowledge about the reality of bio sex is constructed so that we can make the world better for females (safe childbirth, infertility treatments etc), and challenging why social constructs of gender that have no connection to material reality exist at all (gendered clothes, hobbies etc).
But to do that you have to accept that
a. Knowledge about bio sex is constructed but bio sex is not.
b. Knowledge about gender is constructed and gender is wholly constructed.
c. The way we have to challenge issues around bio sex is different to how we challenge things that are solely about gender.
I also think this is complicated by the difference between the radical feminist use of gender and the WHO use of gender. The WHO use of gender could include things about how females teach each other useful knowledge of breastfeeding. That is gendered behaviour, but it isn't oppressive behaviour neccesarily. Under the radical feminist definition of gender as a oppressive system, that behaviour presumably isn't considered gendered. So what is it? Maybe it is like the difference between racism and ethnicity. I don't know.