I agree that the central problem here is that when the WHO or others refer to gender as a social construct, that it implies a social constructionist account of gender. However, I don't see another interpretation that makes much sense. I do precisely think that people can have intentions opposite of the content of their statement, like if a person wanted to reassure a racial minority by telling them that they don't even see race - it sounds supportive, but it communicates a racial eliminativist stance that undermines attempts at justice and repair. Sure, the well-meaning person may not be versed on the nuances of racial eliminativism vs racial constructivism, but it doesn't mean the sentiment isn't still problematic, or that the racial minority is just not understanding the interaction and there must be a mismatch somewhere.

I think the mismatch is between the view being espoused and that person's understanding of the view. Sure, I might smile and nod trying to not soil the interaction, but I don't think the problem is that actually I am mistaken and they aren't communicating a social constructionist account of gender ...

Also, the WHO article does communicate a social constructionist view of gender, and uses the typical gender/sex distinction on the typical basis that gender is social and sex is biological:

Gender refers to the characteristics of women, men, girls and boys that are socially constructed. This includes norms, behaviours and roles associated with being a woman, man, girl or boy, as well as relationships with each other. As a social construct, gender varies from society to society and can change over time.

Gender interacts with but is different from sex, which refers to the different biological and physiological characteristics of females, males and intersex persons, such as chromosomes, hormones and reproductive organs.

This distinction doesn't hold up, as sex is more socially constructed than is acknowledged here, and gender has more of a biological basis than is acknowledged. It is just inaccurate and out of sync with current evidence, as far as I can tell.

Besides the readings I have suggested, another resource covering some of this territory is this lecture:

https://www.youtube.com/watch?v=ZymYiwoRoC0

The chapter around 26 minutes in covers why the sex/gender distinction falls apart.