It actually so far doesn't talk a ton about embroidery directly but there's a lot of interesting things about how notions of gender have evolved. In medieval times (and this is mostly talking about Britain), women were viewed as defective men; this obviously was not great but gave women more freedom than they could later have - a woman could for instance learn a trade so long as it didn't interfere with having kids and stuff, but it was just assumed she'd be worse at it. But it wasn't viewed as a threat to men in the way it later was. Whereas in the Renaissance came the idea that men and women are defined in opposition to each other, that it's the duty of women to be feminine in part because women have to be feminine for men to be masculine. The idea that binary gender as it exists in today's society comes out of the Renaissance is not something I expected.
Also in medieval times, embroidery was more of a communal activity, often done in the service of a church, through projects that required multiple people and someone to plan and direct it. However the association with the church and with nobility meant it was suitable for signaling not just femininity (with embroidery moving from the public to the private sphere) but also social class. This coincided with a move towards the home as an isolated sphere of femininity vs one that overlapped with work (farmwork, workshops etc). After the change towards embroidery being a mark of domesticity it became a way to enforce domesticity: early on in this process women might design patterns that interested them and embroidery was part of a larger (though feminized) education, whereas later on it became part of a preoccupation with making sure everyone was working all the time, and there was a shift towards samplers and towards executing difficult, standardized tasks rather than creativity. Making girls do embroidery, often with messages emphasizing obedience and meekness, became a bigger part of it.
There's also an interesting thing about the story of St Margaret, who is originally said to have killed a dragon and was associated with childbirth, and how her story got censored over time as that was considered unwomanly.