Your assumption relies on the women getting into the field are the best women. I don't see why that would be true. The fields with many women like law, medicine or psychology are much harder to get into than computer science or engineering so most of the best women likely ends up there.
Given that as a woman you don’t benefit from the “competency bias” and constantly has to prove yourself (which is not necessarily bad), combined with the fact that many women simply walk out of careers in computer science and physics because of sexism/harassment, you could consider that the women left are indeed more competent than the average man in the industry.
Women do benefit from likeability bias though, and likeability is certainly a factor when hiring and firing.
As for fake resume studies, the problem with those is that male and female resumes are evaluated differently. If they made a male looking resume and sent it out with a female name it will do badly. But a female looking resume with a male name will also do badly.
What does a male/female looking resume mean? (Genuinely asking. I can't imagine that a female engineering accomplishment is vs a male engineering accomplishment.)
There are plenty of research done on gendered words. Like highlighting your own personal excellence or skill is more masculine etc. There are also of course that men and women tend to have different hobbies and therefore spends their free time doing different things. So one new grad might have done some leadership roles in a horse club while the other maybe did some chess competitions.
Does this mean if you're a woman and you highlight your own personal excellent in your resume you're statistically likely to be treated worse? Similarly if you're a man and you have a leadership role at a horse club you're statistically likely to be treated worse?
Thought experiment: These biases are mostly shared among people so you got them in yourself. Instead of thinking "What is the ideal software engineer", think "what is the ideal feminine software engineer" and "what is the ideal masculine software engineer". The picture in your head will be very different. If you are a woman you will be compared to the ideal feminine engineer while as a man you get compared to the ideal male one.
The prime example is the term "bossy", women get called this since they are expected to be much more cooperative than men. I think a very big issue right now is that we use men as a standard and say "when women use male strategies they get pushback for being too masculine", instead to gain individual success they should try to be like successful women. In an ideal society this wouldn't be the case, but as is these biases exists and so you have to work with them.
And as a personal anecdote, when I looked for jobs as a new grad when I used more cooperative and less personal excellence I didn't get any callbacks. I got lots of callbacks when I focused on personal excellence though. Its as if companies assumed I was less competent just because I talk about teamwork, because their ideal masculine software engineer wouldn't talk like that. You can see here how it works:
Edit: The moral of the story is that when we tell men to be more feminine and women to be more masculine we just hurt them. Men and women aren't evaluated by the same metrics. People told me "Companies expects you to be a teamplayer, try to highlight that!", but it was clearly wrong and didn't help me at all.
I'm curious also, but anecdotally, women were over-represented in my engineering school's societies and probably under-represented in design competitions.
That's the opposite of what happens. My own experience has been that women benefit dramatically from a "being a woman" bias that makes them much more likely to be hired - exactly what this study now quantifies - and in addition be basically unfireable even if they have severe skills or attitude problems.
The whole idea that there's a competency bias towards men is false. What's actually being observed is that women are hired even when they aren't competent, to please feminists and diversity advocates, which then by definition would make men "appear" more competent even if they were of only average competency.
