Remember Orwell’s quote - all men are created equal, some more equal than others”. My guess is that it applies equally to women too.
So the coming gynarchy might be a hierarchical society consisting of four classes.
At the top are strong and dominant alpha women who rule over everyone and decide everything. Maybe comparable to the higher nobility in medieval Europe.
The second class consists of women who , as women , are privileged but have no say in important matters but who owe loyalty and service to the 1st class, maybe working as saleswomen. Comparable to the lower nobility.
The third class would be emasculated males, sissies, who have the privilege of serving women in their homes as housecleaners, gardeners and pretty toys for amusement.
The fourth and lowest class would be stubborn males who would probably be physically emasculated and be kept in stable like quarters and who would have to perform dirty and menial physical tasks.
This is all speculation on my part, but it is so interesting to think about how the coming gynarchy will look like.