The claim in question was "societal pressure placed on women to be accommodating and not be rude and how this can be manipulated to constrain female agency". It seems to me the links you provide are only marginally related. The first is also paywalled, and the last does seem to be an opinion piece. Or does it include some actual data later on (I only looked at the first quarter or so, as it is rather long)? It proposes some experiments, but then goes on with "it is safe to expect result x" - so why even bother proposing experiments?
One example they provide is
(a) "Oh dear, you've put the peanut butter in the refrigerator again."
vs
(b) "Shit, you've put the peanut butter in the refrigerator again."
And we are meant to decide which one was said by a woman. Then it goes on "It is safe to predict that people would classify the first sentence as part of 'women's language', the second as 'men's language'"
Really??? Because women don't say shit (even in 1973)? And men don't say "oh dear"? If that is seminal and what the modern opinion is based on, excuse me for not being impressed.
Edit: just read more of the second link about negotiations. What I see is them just making another unsubstantiated claim ("it's because of socialisation"). But they asked people over the internet when they last negotiated. Have they taken into account that many women perhaps don't even have a job where they get a salary (ie they are house wives)? Or maybe they are more likely to take on jobs that are unionized (teachers, for example), so that the salary is fixed anyway? And so on. Surely there are reasons - maybe it even is socialization, but there is nothing in the articles to substantiate that claim. It is just the author's bias.